International Journal for Numerical Methods in Fluids

Cover image for Vol. 82 Issue 6

Early View (Online Version of Record published before inclusion in an issue)

Edited By: Charbel Farhat, Wolfgang A. Wall

Impact Factor: 1.447

ISI Journal Citation Reports © Ranking: 2015: 17/30 (Physics Fluids & Plasmas); 41/101 (Mathematics Interdisciplinary Applications); 56/104 (Computer Science Interdisciplinary Applications); 62/135 (Mechanics)

Online ISSN: 1097-0363

Associated Title(s): International Journal for Numerical Methods in Biomedical Engineering, International Journal for Numerical Methods in Engineering, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Numerical Linear Algebra with Applications

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  1. 1 - 75
  1. Research Articles

    1. A combined level set/ghost cell immersed boundary representation for floating body simulations

      H. Bihs and A. Kamath

      Version of Record online: 27 SEP 2016 | DOI: 10.1002/fld.4333

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      The paper discusses the implementation of a novel six degree of freedom (6DOF) algorithm in the open-source CFD code REEF3D. The new 6DOF algorithm makes re-meshing or overset grids unnecessary, resulting in a simpler, faster, and more stable algorithm. Several benchmark applications show that the new floating body algorithm can handle even impact scenarios in a weakly coupled manner while maintaining numerical stability and accuracy.

    2. Mono-block and non-matching multi-block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

      A. Resmini, J. Peter and D. Lucor

      Version of Record online: 21 SEP 2016 | DOI: 10.1002/fld.4296

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      The paper presents an enhanced goal-oriented adjoint-based mesh adaptation method based on a scalar indicator for one mesh level only for RANS flows, where the linearization of the Spalart–Allmaras turbulence model is addressed. The adaptation procedure is assessed on standard monoblock and non-conforming multi-block-structured mesh with non-matching interfaces between blocks. The method is efficient for Euler and RANS flows, standard and non-conforming meshes, and transonic and detached subsonic operational flow conditions.

    3. Multi-scale time integration for transient conjugate heat transfer

      L. He and M. Fadl

      Version of Record online: 15 SEP 2016 | DOI: 10.1002/fld.4295

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      A new multi-scale framework in a triple-timing form is adopted to avoid the common quasi-steady flow assumption. Slow temporal variations corresponding to the solid time scales are included in the fluid domain as a source term, whilst short-scale fluid unsteadiness is captured by local time integration. The test case results indicate that a much enhanced applicability can be achieved by relatively small modifications of existing transient conjugate heat transfer methods.

    4. Stabilized mixed three-field formulation for a generalized incompressible Oldroyd-B model

      JaeHyuk Kwack, Arif Masud and K. R. Rajagopal

      Version of Record online: 15 SEP 2016 | DOI: 10.1002/fld.4287

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      A stabilized mixed formulation is developed for a generalized incompressible Oldroyd-B model that is based on a thermodynamically consistent framework for multiple natural configurations. The new method uniformly imposes the incompressibility condition on the elastic stretch tensor and shows optimal L2 convergence for the conformation tensor field on benchmark problems. This figure shows the magnitude of the elastic stretch tensor B and its rate of convergence for various element types.

  2. Editorials

  3. Research Articles

    1. GPU-accelerated direct numerical simulations of decaying compressible turbulence employing a GKM-based solver

      Nishant Parashar, Balaji Srinivasan, Sawan Suman Sinha and Manish Agarwal

      Version of Record online: 8 SEP 2016 | DOI: 10.1002/fld.4291

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      Evaluation of the analytical gas kinetic method developed by Xuan and Xu (2013) is done in its performance to simulate decaying compressible turbulence on graphical processing unit (GPU)s. We find that analytical gas kinetic method results show excellent agreement with high-order accurate direct numerical simulation results. We perform GPU optimizations on NVIDIA K20 GPU, which boosts the speedup up-to 40x as compared with CPU computations.

    2. Turbulence modelling and role of compressibility on oil spilling from a damaged double hull tank

      Hao Yang, Shiqiang Yan, Qingwei Ma, Jinshu Lu and Yan Zhou

      Version of Record online: 7 SEP 2016 | DOI: 10.1002/fld.4294

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      The paper presents comparative studies on the turbulence modelling and the role of compressibility on oil spilling from DHTs. It suggests criterion to select the appropriate turbulence model in terms of computational robustness using the effective Reynolds number, considering both oil outflow and water inflow. It also concludes that the compressibility of the fluid may be considerable in a small temporal-spatial scale but plays insignificant role on macroscopic process of the oil spilling.

    3. A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system

      D. Mitsotakis, C. Synolakis and M. McGuinness

      Version of Record online: 6 SEP 2016 | DOI: 10.1002/fld.4293

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      A fully discrete numerical scheme for some fully-nonlinear shallow water equations with wall boundary conditions is developed. Shoaling and reflecting solitary waves are studied in detail. The accuracy and the efficiency of this numerical method is demonstrated while the match between numerical results, experimental data, and theoretical approximations is very satisfactory.

  4. Research Paper Presented at MULTIMAT 2015

    1. High-order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics

      M. Holec, J. Limpouch, R. Liska and S. Weber

      Version of Record online: 5 SEP 2016 | DOI: 10.1002/fld.4288

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      Nonlocal radiative transport in laser-heated plasmas of arbitrary Knudsen number is a challenging task. We directly solve the photon transport equation based on the Bhatnagar-Gross-Krook(BGK) collision operator, which gives an inherent coupling of radiation to the fluid plasma parameters. Our high-order discontinuous Galerkin scheme of the BGK transport equation and thefluid energy equation gives solutions obeying both limiting cases of transport, i.e. diffusion and free-streaming. As an application, we present simulation results of intense laser-target interaction.

    2. A fully discrete ALE method over untwisted time–space control volumes

      Jin Qi and Jiequan Li

      Version of Record online: 24 AUG 2016 | DOI: 10.1002/fld.4283

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      Our work is focused on two important technologies in ALE method:

      • The untwisted adaptively moving time–space control volume is generated only by the irrotational part of the flow velocity based on the Helmholtz theorem to avoid the mesh tangling.
      • The GRP solver with the whole wave configuration is employed for flux computation to ensure the high resolution.
    3. Divergence preserving reconstruction of the nodal components of a vector field from its normal components to edges

      Richard Liska and Mikhail Shashkov

      Version of Record online: 22 AUG 2016 | DOI: 10.1002/fld.4289

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      We have developed a new divergence preserving method for the reconstruction of the Cartesian components of a vector field from the orthogonal projection of a vector field to the normals to edges in 2D. The new global divergence preserving method is exact for linear vector fields.

  5. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. Parallel implementation of data assimilation

      Alexander Bibov and Heikki Haario

      Version of Record online: 21 AUG 2016 | DOI: 10.1002/fld.4278

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      Kalman filter is a known sequential algorithm that allows to estimate states of dynamical systems using predicted a-priori information and observed data. However, due to its sequential nature the algorithm cannot be efficiently implemented on parallel systems and suffers from memory and performance issues when dimension of the state space becomes large. In the present paper we alleviate these problems by using certain approximation of the filter and reformulating the classical filtering task to allow for parallelism.

  6. Research Articles

    1. Smoothed-profile method for momentum and heat transfer in particulate flows

      Francesco Romanò and Hendrik C. Kuhlmann

      Version of Record online: 19 AUG 2016 | DOI: 10.1002/fld.4279

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      The smoothed-profile method combined with a discontinuous Galerkin finite-element method is investigated for simulating the motion of solid bodies in a fluid phase. Different smoothed-profile functions are compared and the algorithm is extended to include thermal effects. The solver is benchmarked against theoretical and experimental results for several problems.

    2. A simple phase transition relaxation solver for liquid–vapor flows

      Alexandre Chiapolino, Pierre Boivin and Richard Saurel

      Version of Record online: 17 AUG 2016 | DOI: 10.1002/fld.4282

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      This work presents a new method to compute thermochemical equilibrium in liquid–vapor flows. The proposed method is both accurate and fast, in addition of being much easier to code than the usual iterative methods. Through a series of test cases from simple 1D flow configurations to a complex 2D evaporating liquid jet, the solver is proved to successfully cope with cavitation, evaporation, condensation, and boiling.

  7. Research Paper Presented at MULTIMAT 2015

    1. Study of a collocated Lagrange-remap scheme for multi-material flows adapted to HPC

      Jean-Philippe Braeunig and Bastien Chaudet

      Version of Record online: 17 AUG 2016 | DOI: 10.1002/fld.4286

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      In the context of a Eulerian Lagrange-remap scheme on planar geometry and for rectangular meshes, we propose and compare remapping schemes using a finite volume framework. We consider directional splitting or fully multi-dimensional remaps, and we focus on a definition of the so-called corner fluxes. We also address the issue of the internal energy behavior when using a conservative total energy remap.

  8. Research Articles

    1. A rotating reference frame-based lattice Boltzmann flux solver for simulation of turbomachinery flows

      Di Zhou, Zhiliang Lu and Tongqing Guo

      Version of Record online: 12 AUG 2016 | DOI: 10.1002/fld.4281

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      A promising lattice Boltzmann flux solver (LBFS) is developed into a version in the rotating frame of reference for simulation of turbomachinery flows. Since the numerical fluxes at the cell interface are evaluated by reconstructing local solution of lattice Boltzmann equation, it has a delicate dissipation mechanism and is thus free of additional artificial fixes. Numerical tests for several typical turbomachinery flows with different complexities demonstrate the accuracy and robustness of the present method.

    2. A novel weighting switch function for uniformly high-order hybrid shock-capturing schemes

      Jun Peng and Yiqing Shen

      Version of Record online: 10 AUG 2016 | DOI: 10.1002/fld.4285

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      In this paper, a parameter-free weighting switch function is proposed for developing a family of high order hybrid schemes. As an example, a seventh-order hybrid compact-CRWENO scheme (HCCS) is constructed and analyzed with the proposed function. Numerical results show that the new scheme has very low dissipation and maintains the essentially non-oscillation property of the base-CRWENO scheme. As shown in this figure, HCCS is even more efficient than the seventh-order WENO scheme.

  9. Research Paper Presented at MULTIMAT 2015

    1. A 3D finite element ALE method using an approximate Riemann solution

      V. P. Chiravalle and N. R. Morgan

      Version of Record online: 9 AUG 2016 | DOI: 10.1002/fld.4284

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      A finite element arbitrary Lagrangian–Eulerian method that solves a multidirectional Riemann-like problem incorporating two limiting coefficients: the first is based on the minmod limiter and the second is a function of the discrete Mach number is presented. Our approach produces substantially less internal energy errors than the minmod limiter alone for a steel shell implosion as shown in Figure 1. For strong shock problems, the new limiter is more accurate and converges at a higher rate than the quadratic artificial viscosity.

  10. Research Articles

    1. Interface transport scheme of a two-phase flow by the method of characteristics

      Mireille Haddad, Frédéric Hecht and Toni Sayah

      Version of Record online: 8 AUG 2016 | DOI: 10.1002/fld.4280

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      In this paper, we propose an interface transport scheme of a two-phase flow for an incompressible viscous immiscible fluid of large-density ratio to model 3D molds filling. A new natural boundary condition under pressure effect for the transport equation is proposed. Finally, numerical validations show the effectiveness of the proposed scheme.

    2. On parallel pre-conditioners for pressure Poisson equation in LES of complex geometry flows

      K. M. Singh, E. J. Avital, J. J. R. Williams, C. Ji, X. Bai and A. Munjiza

      Version of Record online: 8 AUG 2016 | DOI: 10.1002/fld.4277

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      Large eddy simulation of non-uniform Cartesian grids and the immersed boundary method is used for incompressible turbulent flow simulations of complex geometry bodies. Acceleration of the pressure Poisson equation's solution is sought. The present work has brought forth two new aspects: (a) a geometric multigrid preconditioner for pressure Poisson equation in an immersed boundary Navier–Stokes solver on stretched grids and (b) efficacy of the simple SOR(k) preconditioner for highly stretched grids.

  11. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. You have full text access to this OnlineOpen article
      A variational ensemble Kalman filtering method for data assimilation using 2D and 3D version of COHERENS model

      Idrissa Amour and Tuomo Kauranne

      Version of Record online: 4 AUG 2016 | DOI: 10.1002/fld.4276

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      In ensemble data assimilation, such as the variational ensemble Kalman filter, increasing ensemble size does not always improve the analysis, as is seen in the figures attached that depict the truth and analysis with 10, 30, and 50 ensemble members. This phenomenon emphasizes the property of data assimilation that innovation is often captured in a much lower-dimensional space than the entire state space. Variational ensemble Kalman filter automatically identifies such a low-dimensional space.

  12. Research Articles

    1. You have full text access to this OnlineOpen article
      A force-balanced control volume finite element method for multi-phase porous media flow modelling

      J. L. M. A. Gomes, D. Pavlidis, P. Salinas, Z. Xie, J. R. Percival, Y. Melnikova, C. C. Pain and M. D. Jackson

      Version of Record online: 4 AUG 2016 | DOI: 10.1002/fld.4275

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      Multi-phase flow through highly permeable underground channels (the flow is from the left). The novel method presented and validated in this paper allows for discontinuous description of pressure and saturation between elements which results in minimal numerical dispersion. In addition, the method is high-order accurate and uses fully unstructured meshes as shown in thefigure.

    2. Discharge estimation under uncertainty using variational methods with application to the full Saint-Venant hydraulic network model

      Igor Gejadze and Pierre-Olivier Malaterre

      Version of Record online: 28 JUL 2016 | DOI: 10.1002/fld.4273

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      The paper presents a novel version of variational data assimilation (DA) approach designed for solving estimation-under-uncertainty problems. A modified iterative process which guaranties regular convergence is used. This is vitally important if the model domain (i.e. the set of the control/parameter values for which the model solution exist) is bounded. The method is applied for solving discharge estimation problem under uncertainty in bathymetry and the friction coefficient involving SIC2, which is the full Saint-Venant hydraulic network model of a commercial status.

  13. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. Sensitivity analysis applied to a variational data assimilation of a simulated pollution transport problem

      F.-X. Le Dimet, I. Souopgui and H. E. Ngodock

      Version of Record online: 25 JUL 2016 | DOI: 10.1002/fld.4274

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      In the presence of variational data assimilation, the sensitivity analysis must be carried on the optimality system. The sensitivity on the optimality system captures the indirect effects of the variation of the source on the response function, which is not possible with the sensitivity analysis on the model alone.

  14. Research Articles

    1. On the immersed boundary-lattice Boltzmann simulations of incompressible flows with freely moving objects

      Y. Wang, C. Shu, L. M. Yang and Y. Sun

      Version of Record online: 25 JUL 2016 | DOI: 10.1002/fld.4270

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      • The paper presents an immersed boundary-lattice Boltzmann flux solver in the arbitrary Lagrangian–Eulerian coordinates for simulating solid objects falling freely in unbounded domains;
      • A dynamic similarity theory is introduced for the lattice Boltzmann schemes to achieve the incompressible condition;
      • The proposed solver and dynamic similarity theory are successfully validated by simulating several challenging benchmark problems, including freely falling plate as shown in the figure.
  15. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. Reduced rank static error covariance for high-dimensional applications

      Milija Zupanski

      Version of Record online: 21 JUL 2016 | DOI: 10.1002/fld.4264

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      A method for creating static error covariance of reduced rank for potential use in hybrid variational-ensemble data assimilation is presented, based on the use of singular value decomposition and circulant matrices. The main benefit of the reduced rank error covariance is in improving the Hessian preconditioning in high-dimensional applications. The results show that it may be possible to reduce the rank of matrix from O(105) to O(10) and still obtain an acceptable approximation of the full-rank static covariance matrix.

    2. Reduced-order modeling for nonlocal diffusion problems

      David R. Witman, Max Gunzburger and Janet Peterson

      Version of Record online: 18 JUL 2016 | DOI: 10.1002/fld.4269

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      We present a novel reduced-order approach to the one-dimensional nonlocal anomalous diffusion problem. Results show good convergence of the POD-ROM method at approximating the nonlocal solution in a few different problem settings.

    3. An efficient goal-based reduced order model approach for targeted adaptive observations

      F. Fang, C. C. Pain, Ionel M. Navon and D. Xiao

      Version of Record online: 12 JUL 2016 | DOI: 10.1002/fld.4265

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      An efficient adjoint sensitivity technique for optimally collecting targeted observations is presented. The targeting technique incorporates dynamical information from the numerical model predictions to identify when, where, and what types of observations would provide the greatest improvement to specific model forecasts at a future time. A functional (goal) is defined to measure what is considered important in modelling problems. The adjoint sensitivity technique is used to identify the impact of observations on the predictive accuracy of the functional, then placing the sensors at the locations with high impacts. The adaptive (goal) observation technique developed here has the following features: (1) over existing targeted observation techniques, its novelty lies in that the interpolation error of numerical results is introduced to the functional (goal) which ensures the measurements are a distance apart; (2) the use of proper orthogonal decomposition (POD) and reduced order modelling (ROM) for both the forward and backward simulations, thus reducing the computational cost; and (3) the use of unstructured meshes.

  16. Research Articles

    1. Uncertainty quantification in LES of channel flow

      Cosmin Safta, Myra Blaylock, Jeremy Templeton, Stefan Domino, Khachik Sargsyan and Habib Najm

      Version of Record online: 12 JUL 2016 | DOI: 10.1002/fld.4272

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      We present a Bayesian framework for estimating joint densities for large eddy simulation sub-grid scale model parameters based on canonical forced isotropic turbulence direct numerical simulation data. Posterior densities for sub-grid scale model parameters are then propagated forward through large eddy simulation of channel flow and compared to channel flow direct numerical simulation data.

    2. A semi-Lagrangian multi-moment finite volume method with fourth-order WENO projection

      Ziyao Sun and Feng Xiao

      Version of Record online: 11 JUL 2016 | DOI: 10.1002/fld.4271

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      This paper presents a novel algorithm that introduces a nodal value-based WENO limiter for CIP/MM FVM as a trial to pursue a better suited formulation to implement the limiting projection in schemes with local DOFs. The new scheme, CIP-CSL-WENO4 scheme, which is free of the ad hoc TVB ‘trouble cell’ indicator can achieve superior accuracy compared with Eulerian formulation due to its semi-Lagrangian nature. The numerical results of benchmark tests show excellent solution quality compared with other existing schemes.

  17. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. Non-intrusive reduced order modelling with least squares fitting on a sparse grid

      Z. Lin, D. Xiao, F. Fang, C. C. Pain and Ionel M. Navon

      Version of Record online: 8 JUL 2016 | DOI: 10.1002/fld.4268

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      This paper presents a non-intrusive reduced order model (NIROM) for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. Then we introduce a new least squares fitting procedure to approximate the dynamical transition of the POD coefficients between subsequent time steps, taking only a set of full model solution snapshots as the input. Thus, the physics and numerics of the original PDE model are fully transparent to this methodology, and its level of non-intrusiveness is improved compared with existing reduced order models. Furthermore, we take adaptive measures to address the instability issue arising from reduced order iterations of the POD coefficients. This model can be applied to a wide range of physical and engineering scenarios, and we test it on a couple of problems in fluid dynamics. It is demonstrated that this reduced order approach captures the dominant features of the high fidelity models with reasonable accuracy while the computation complexity is reduced by several orders of magnitude.

    2. Optimal solution error quantification in variational data assimilation involving imperfect models

      V. Shutyaev, I. Gejadze, A. Vidard and F.-X. Le Dimet

      Version of Record online: 4 JUL 2016 | DOI: 10.1002/fld.4266

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      The paper presents a generic methodology for assessing the optimal solution error covariance matrix in data assimilation involving imperfect models. We consider both the strong constraint and weak constraint variational data assimilation formulations. The later includes a dynamical model describing the model error evolution. In the first case, the covariance is approximated by the inverse Hessian, whereas in the second case, a special formula has been derived. The theory is verified by numerical tests involving the one-dimensional Burgers' equation.

  18. Research Articles

    1. Validation of the S-CLSVOF method with the density-scaled balanced continuum surface force model in multiphase systems coupled with thermocapillary flows

      Takuya Yamamoto, Yasunori Okano and Sadik Dost

      Version of Record online: 30 JUN 2016 | DOI: 10.1002/fld.4267

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      Three numerical methods for multiphase flow with thermocapillary flow were validated for their accuracy by using OpenFOAM: volume of fluid, simple coupled volume of fluid with level set (S-CLSVOF), and S-CLSVOF with density-scaled balanced continuum surface force (CSF) model. Results have shown that the S-CLSVOF method gives accurate results, and S-CLSVOF method with density-scaled balanced CSF model leads to accurate results in the cases of large interface deformations and large density and viscosity ratios.

  19. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. Non-intrusive reduced-order modeling for multiphase porous media flows using Smolyak sparse grids

      Dunhui Xiao, Zhi Lin, Fangxin Fang, Christopher C. Pain, Ionel M. Navon, Pablo Salinas and Ann Muggeridge

      Version of Record online: 23 JUN 2016 | DOI: 10.1002/fld.4263

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      In this article, we describe a non-intrusive reduction method for porous media multiphase flows using Smolyak sparse grids.This is the first attempt at applying such an non-intrusive reduced order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high-fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude.

      The figures displayed earlier (left) show the saturation solutions of the high-permeability domain embedded in a low-permeability domain problem at time instances 0.05. The solutions compare the predictions from non-intrusive reduced order model with high-fidelity full model using 36 proper orthogonal decomposition basis functions.

    2. Efficient approximation of Sparse Jacobians for time-implicit reduced order models

      Răzvan Ştefănescu and Adrian Sandu

      Version of Record online: 23 JUN 2016 | DOI: 10.1002/fld.4260

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      This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The method uses only samples of the nonzero entries of the matrix series. The sparse matrix approximation strategy is compared against various existing methods for computing reduced Jacobians in the case of the 1D Burgers and 2D shallow water equations models.

    3. POD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems

      Francesco Ballarin and Gianluigi Rozza

      Version of Record online: 21 JUN 2016 | DOI: 10.1002/fld.4252

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      We propose a monolithic approach for reduced order modeling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition—Galerkin method. Parameters are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. The parametrized formulation of the multiphysics problem, and efficient offline—online computational procedure, are introduced. Several numerical results highlight the capabilities of the proposed reduced order method and its computational performances.

  20. Research Articles

    1. An improved ghost-cell immersed boundary method for compressible flow simulations

      Cheng Chi, Bok Jik Lee and Hong G. Im

      Version of Record online: 17 JUN 2016 | DOI: 10.1002/fld.4262

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      We present an improved ghost-cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work, ghost cells are mirrored through the boundary described using a level-set method to farther image points, incorporating a higher-order extrapolation/interpolation scheme for the ghost-cell values. Direct comparisons against the cut-cell method demonstrate that the present method is almost equally accurate with better efficiency for boundary representation in high-fidelity compressible flow simulations.

  21. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. The method of dynamic mode decomposition in shallow water and a swirling flow problem

      Diana A. Bistrian and Ionel M. Navon

      Version of Record online: 16 JUN 2016 | DOI: 10.1002/fld.4257

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      We propose a new criterion for dynamic modes selection that is able to extract dynamically relevant flow features from dynamic mode decomposition of time-resolved experimental or numerical data. We employ a novel modes selection criterion in parallel with the classic selection based on modes amplitudes. Numerical tests are performed on two distinct problems. The efficiency of the proposed criterion is proved in retaining the most influential modes and reducing the size of the dynamic mode decomposition model.

  22. Research Articles

    1. A higher resolution edge-based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

      Rogério Soares da Silva, Paulo Roberto Maciel Lyra, Ramiro Brito Willmersdorf and Darlan Karlo Elisiário de Carvalho

      Version of Record online: 16 JUN 2016 | DOI: 10.1002/fld.4254

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      In this article, we present a higher-order finite volume method with a ‘Modified Implicit Pressure, Explicit Saturation’ formulation to model the 2D incompressible and immiscible two-phase flow of oil and water in heterogeneous and anisotropic porous media. Our higher-order formulation produces very accurate solutions with a sharp front resolution and less grid orientation effects than the traditional first-order upwind method at a reasonable computational cost.

  23. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. The reduced-order hybrid Monte Carlo sampling smoother

      Ahmed Attia, Răzvan Ştefănescu and Adrian Sandu

      Version of Record online: 15 JUN 2016 | DOI: 10.1002/fld.4255

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      We introduce computationally efficient versions of the hybrid Monte Carlo sampling smoother based on reduced-order approximations of the underlying model dynamics. These reduced versions are capable of accurately capturing the posterior probability density while being significantly faster than the original full-order formulation. The proposed methods are sampling a fully projected posterior and the high-fidelity posterior distribution with approximate gradient using a reduced-order model.

    2. A Hybrid Monte-Carlo sampling smoother for four-dimensional data assimilation

      Ahmed Attia, Vishwas Rao and Adrian Sandu

      Version of Record online: 14 JUN 2016 | DOI: 10.1002/fld.4259

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      We introduce an ensemble-based sampling smoother for four-dimensional data assimilation using a Hybrid/Hamiltonian Monte-Carlo approach. The Hybrid/Hamiltonian Monte-Carlo sampling smoother naturally accommodates non-Gaussian errors and nonlinear model dynamics and observation operators. The proposed methodology can provide a consistent and accurate approximation of the posterior distribution in the non-Gaussian data assimilation framework.

    3. Sensitivity-guided decision-making for wind farm micro-siting

      Fatma Ulker, Douglas Allaire and Karen Willcox

      Version of Record online: 10 JUN 2016 | DOI: 10.1002/fld.4256

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      This paper presents a quantitative risk assessment for design and development of a renewable energy system to support decision-making among design alternatives. Throughout the decision-making phases, resources are allocated amongst exploration and exploitation tasks to manage the uncertainties in design parameters and to adapt designs to new information for enhanced performance. The resource allocation problem is formulated as a sequential decision feedback loop that is guided by global and regional sensitivity analyses.

    4. Efficient computation of operator-type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

      Dan G. Cacuci, Aurelian F. Badea, Madalina C. Badea and James J. Peltz

      Version of Record online: 9 JUN 2016 | DOI: 10.1002/fld.4258

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      The predictive modeling methodology developed by Cacuci and Ionescu-Bujor (2010) is applied to a spent nuclear fuel dissolver model to obtain best-estimate values for predicted model responses (e.g., acid concentrations) and parameters (e.g., time-dependent inlet boundary conditions), with reduced predicted uncertainties. The adjoint sensitivity analysis methodology for operator-valued responses developed by Cacuci (1981) is used for computing most efficiently the response sensitivities needed for the accompanying uncertainty quantification, data assimilation, and model calibration.

  24. Research Articles

    1. Curvilinear smoothed particle hydrodynamics

      Sasan Tavakkol, Amir Reza Zarrati and Mahdiyar Khanpour

      Version of Record online: 7 JUN 2016 | DOI: 10.1002/fld.4261

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      We suggest a new set of equations to employ smoothed particle hydrodynamics (SPH) in a curvilinear space, and we refer to it as curvSPH. The new method makes the horizontal and vertical resolutions independent from each other. It also provides capability to model curved boundaries as straight lines. Different simulations, including simulation of a flip bucket are performed to demonstrate the applicability of the proposed method. Good agreement of results with experimental data and classical SPH confirms the capabilities of curvSPH.

    2. 2D Burgers equation with large Reynolds number using POD/DEIM and calibration

      Yuepeng Wang, Ionel M. Navon, Xinyue Wang and Yue Cheng

      Version of Record online: 1 JUN 2016 | DOI: 10.1002/fld.4249

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      For the 2D Burgers equation with large Reynolds number (turbulent flow case), we have developed the proper orthogonal decomposition/discrete empirical interpolation method-reduced order model and provided detailed solution. A flow calibration with Tikhonov regularization serving as closure model is also carried out in order to recover the turbulent closure. The computational results exhibit considerable agreement with the real high-fidelity model.

    3. A spectral-element discontinuous Galerkin thermal lattice Boltzmann method for conjugate heat transfer applications

      Saumil Patel, Misun Min and Taehun Lee

      Version of Record online: 29 MAY 2016 | DOI: 10.1002/fld.4250

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      This graphic shows isotherms for Gr = 106 in a horizontal annulus using the proposed spectral-element discontinuous Galerkin thermal lattice Boltzmann method. Using the discrete Boltzmann equations for nearly incompressible, thermal flows, the spectral-element discontinuous Galerkin thermal lattice Boltzmann method is able to solve fluid–solid conjugate heat transfer applications on unstructured, non-uniform grids. Bounce-back boundary conditions are imposed via the numerical flux formulation that arises because of the discontinuous Galerkin approach. This scheme does not require tedious extrapolation at the boundaries that may cause loss of mass conservation.

    4. A mass conservative well-balanced reconstruction at wet/dry interfaces for the Godunov-type shallow water model

      Martin Fišer, Ilhan Özgen, Reinhard Hinkelmann and Jan Vimmr

      Version of Record online: 26 MAY 2016 | DOI: 10.1002/fld.4246

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      The paper presents a new numerical method for the shallow water equations. The article describes computing of the bed slope source term, which is well balanced not only in the flooded domain but also in the wet/dry interface. The scheme is capable to compute the flow of the water depth approaching zero value without loss of the accuracy. Moreover, the resulting scheme is also mass conservative.

    5. You have full text access to this OnlineOpen article
      SPH modelling of depth-limited turbulent open channel flows over rough boundaries

      Ehsan Kazemi, Andrew Nichols, Simon Tait and Songdong Shao

      Version of Record online: 25 MAY 2016 | DOI: 10.1002/fld.4248

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      We have significantly improved the turbulence modelling and rough boundary treatment to enable the smoothed particle hydrodynamics method to work in depth-limited open channel uniform flows over a rough bed surface with a robust technique for the inflow and outflow boundaries. The computed velocity and shear stress profiles are found to be in good agreement with the experimental data measured in a laboratory flume with a well-packed bed of uniform-sized spheres.

  25. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. Ensemble data assimilation applied to an adaptive mesh ocean model

      Juan Du, Jiang Zhu, Fangxin Fang, C. C. Pain and I. M. Navon

      Version of Record online: 25 MAY 2016 | DOI: 10.1002/fld.4247

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      The adaptive mesh ensemble Kalman filter data assimilation system was established and tested in this work. The unstructured mesh was adapted with respect to both the state variable and the observation locations. The conservative mesh generation technique ‘supermesh’ was adopted to deal with the different meshes on which the ensembles were defined. It is proved that the adaptive mesh ensemble Kalman filter data assimilation system had a positive effect on the model results.

  26. Research Articles

    1. High-order strand grid methods for low-speed and incompressible flows

      Jonathan Thorne, Aaron Katz, Oisin Tong, Yushi Yanagita, Yoshiharu Tamaki and Keegan Delaney

      Version of Record online: 24 MAY 2016 | DOI: 10.1002/fld.4251

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      In this paper, we address a number of challenges associated with the computation of low-speed and incompressible flows through the use of automated strand grid generation, unique high-order methods, and preconditioning. We explore a preconditioned flux correction method for unstructured layers of the strand grid coupled together using a source term containing summation-by-parts finite differences in the strand direction. Laminar flow test cases indicate dramatic improvements in accuracy and convergence using the high-order preconditioned method, while turbulent body-ofrevolution flow results show improvements in only some cases, perhaps because of dominant errors arising from the turbulence model itself.

    2. Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries

      Alexandre Cameron, Raphaël Raynaud and Emmanuel Dormy

      Version of Record online: 20 MAY 2016 | DOI: 10.1002/fld.4245

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      Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont & Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.

    3. Residual-based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics

      Oriol Guasch, Patricia Sánchez-Martín, Arnau Pont, Joan Baiges and Ramon Codina

      Version of Record online: 18 MAY 2016 | DOI: 10.1002/fld.4243

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      This paper presents a stabilized finite element method (FEM) for the acoustic perturbation equations (APE) at low Mach numbers. The proposed stabilized formulation allows one to retain all convective and reaction terms in the APE and to deal with acoustic waves propagating in solenoidal mean flows with non-uniform convection and shear. The numerical examples reveal the contributions of the various terms in the APE and the importance not to neglecting them in many aeroacoustic problems.

  27. Virtual Special Issue Paper on Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. Spectral characteristics of background error covariance and multiscale data assimilation

      Zhijin Li, Xiaoping Cheng, William I. Gustafson Jr. and Andrew M. Vogelmann

      Version of Record online: 17 MAY 2016 | DOI: 10.1002/fld.4253

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      Data assimilation algorithms derived from optimal estimation theory hinge on the background error covariance. Numerical analyses show that the background error correlation length scale is about 75 km for the streamfunction (left), even with a model at a horizontal resolution of 2 km. With this correlation scale, the spectral power density of the background errors are virtually zero for scales smaller than 150 km, which is twice the correlation length scale (right). Thus, data assimilation algorithms are unable to correct background errors at least for horizontal scales smaller than the twice correlation length scale. A multiscale variational data assimilation scheme is suggested to estimate distinct scales separately for high-resolution models.

  28. Research Articles

    1. Structural–acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme

      Leilei Chen, Haibo Chen, Changjun Zheng and Steffen Marburg

      Version of Record online: 10 MAY 2016 | DOI: 10.1002/fld.4244

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      This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. Discontinuous higherorder boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis.

    2. An improved Rhie–Chow interpolation scheme for the smoothed-interface immersed boundary method

      Wei Yi, Daniel Corbett and Xue-Feng Yuan

      Version of Record online: 10 MAY 2016 | DOI: 10.1002/fld.4240

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      A fully parallelized smoothed-interface immersed boundary method on a co-located grid is described. An improved Rhie–Chow interpolation scheme is proposed to increase the accuracy in resolving the flow near the immersed boundary. It is validated by benchmark test results of flow past a stationary/oscillating cylinder.

    3. Fitted finite element discretization of two-phase Stokes flow

      Marco Agnese and Robert Nürnberg

      Version of Record online: 10 MAY 2016 | DOI: 10.1002/fld.4237

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      We propose an unconditionally stable fitted finite element method for two-phase Stokes flow that uses piecewise linear finite elements to approximate the moving interface. Our numerical approximation captures exactly spherical stationary solutions. Moreover, the meshes describing the discrete interface in general do not deteriorate in time. Therefore, it is not necessary to smooth or to remesh them during the numerical simulations. We present several numerical experiments which demonstrate the accuracy and robustness of the proposed algorithm.

    4. Improvement of multistep WENO scheme and its extension to higher orders of accuracy

      Yankai Ma, Zhenguo Yan and Huajun Zhu

      Version of Record online: 6 MAY 2016 | DOI: 10.1002/fld.4242

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      A new class of multistep WENO methods is presented through using new modified nonlinear weights. The weights definition takes into account the novel extra information on the regularity of the solution and renders smoothness indicators closer to uniformity so as to increase the resolution power when approximating smooth solutions. This new method provides WENO schemes with enhanced order of convergence at transition points while maintaining stability and the ENO behavior.

    5. Multiscale coupling of compliant and rigid walls blood flow models

      Tatiana Dobroserdova, Maxim Olshanskii and Sergey Simakov

      Version of Record online: 5 MAY 2016 | DOI: 10.1002/fld.4241

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      Pressure distribution for steady problem of detonation with Cochran-Chan equation of state, with the variables reconstruction for mixing fluids, we obtain an accurate convergence solution.

    6. A gas-kinetic scheme for the simulation of turbulent flows on unstructured meshes

      Dongxin Pan, Chengwen Zhong, Ji Li and Congshan Zhuo

      Version of Record online: 5 MAY 2016 | DOI: 10.1002/fld.4239

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      Coupling gas-kinetic scheme with Spalart–Allmaras turbulence model, a finite volume method is introduced for the solution of turbulent flow. To organize the unstructured mesh data structure efficiently, a non-manifold hybrid mesh data structure is extended for polygonal cells. The adaptive mesh refinement technique is also adopted to reduce computational cost and improve the efficiency of meshes. Numerical experiments are performed on incompressible flow over a smooth flat plate and compressible turbulent flow around a NACA 0012 airfoil.

    7. Simulation of anisotropic diffusion processes in fluids with smoothed particle hydrodynamics

      Thien Tran-Duc, Erwan Bertevas, Nhan Phan-Thien and Boo Cheong Khoo

      Version of Record online: 27 APR 2016 | DOI: 10.1002/fld.4238

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      A new smoothed particle hydrodynamics (SPH) approximation for diffusion operator, named anisotropic SPH approximation for anisotropic diffusion (ASPHAD), is derived. ASPHAD is general and unique for both isotropic and anisotropic diffusions with either constant or variable diffusin coefficients. Numerical examinations in some cases of isotropic and anisotropic diffusions of a contaminant in fluid show a very good consistence with corresponding analytical solutions.

    8. Multi-material closure model for high-order finite element Lagrangian hydrodynamics

      V. A. Dobrev, T. V. Kolev, R. N. Rieben and V. Z. Tomov

      Version of Record online: 27 APR 2016 | DOI: 10.1002/fld.4236

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      We present a closure model that evolves material properties at quadrature point level. The method is general with respect to the number of materials, dimension and space and time discretizations.Material volumes are evolved by imposing partial pressure equilibration, and internal energy exchange between materials is determined by considerations of the expected behavior of the entropy production. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material arbitrary Lagrangian-Eulerian high-velocity impacts.

    9. A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

      X. Gao, L. D. Owen and S. M. J. Guzik

      Version of Record online: 21 APR 2016 | DOI: 10.1002/fld.4235

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      A fourth-order finite-volume method for solving the Navier-Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. Shown here, a Mach reflection problem is solved to demonstrate the effectiveness of the mapped algorithm on a non-rectangular physical domain. AMR patches on the finest mesh level are outlined.

    10. A variable-fidelity aerodynamic model using proper orthogonal decomposition

      M. J. Mifsud, D. G. MacManus and S.T. Shaw

      Version of Record online: 20 APR 2016 | DOI: 10.1002/fld.4234

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      A variable-fidelity aerodynamic model based on proper orthogonal decomposition (POD) of an ensemble of computational fluid dynamics (CFD) solutions at variable fidelity and at different parameters is presented in this article. This approach is used to predict supersonic flow over a slender configuration using Navier–Stokes solutions that are computed at two different levels of nominal accuracy as the low-fidelity and high-fidelity solutions. The numerical results show that the proposed model is efficient and sufficiently accurate.

    11. An efficient numerical method for reactive flow with general equation of states

      Xianyang Zeng, Min Xiao and Guoxi Ni

      Version of Record online: 14 APR 2016 | DOI: 10.1002/fld.4233

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      Pressure distribution for steady problem of detonation with Cochran-Chan equation of state, with the variables reconstruction for mixing fluids, we obtain an accurate convergence solution.

  29. Review Articles

    1. Well-balanced finite difference weighted essentially non-oscillatory schemes for the blood flow model

      Zhenzhen Wang, Gang Li and Olivier Delestre

      Version of Record online: 31 MAR 2016 | DOI: 10.1002/fld.4232

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      A high-order well-balanced finite difference weighted essentially non-oscillatory scheme is designed for the blood flow model. The scheme preserves the well-balanced property and achieves high-order accuracy for smooth solutions. In addition, the scheme possesses sharp shock transition.

  30. Research Articles

    1. A class of finite difference schemes for interface problems with an HOC approach

      H. V. R. Mittal, Jiten C. Kalita and Rajendra K. Ray

      Version of Record online: 28 MAR 2016 | DOI: 10.1002/fld.4231

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      A class of efficient higher order accurate finite difference schemes is developed for parabolic and elliptic PDEs with discontinuous coefficients and singular source terms. Clubbing a recently developed HOC methodology with special interface treatment renders the schemes at least a second order spatial accuracy. Apart from 1D problems, the 2D extension of the schemes works with equal ease on problems in polar and Cartesian grids. Excellent results are obtained including the famous von Kármán vortex street for flow past circular cylinder.

    2. A spectral/hp least-squares finite element analysis of the Carreau–Yasuda fluids

      Namhee Kim and J. N. Reddy

      Version of Record online: 17 MAR 2016 | DOI: 10.1002/fld.4230

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      A mixed least-squares finite element model with spectral/hp approximations was developed for steady, two-dimensional flows of non-Newtonian fluids obeying the Carreau-Yasuda constitutive model. The mixed least-squares finite element model developed herein has advantages over the weak-form Galerkin model in eliminating any type of locking. In addition, there are no compatibility restrictions placed between velocity, pressure, and stress approximation spaces for sufficiently higher-order polynomials. Also, a combination of spectral/hp approximation functions and least-squares model yields accurate results with spectral convergence.

    3. Bubble-based stabilized finite element methods for time-dependent convection–diffusion–reaction problems

      A. Sendur and A. Nesliturk

      Version of Record online: 7 MAR 2016 | DOI: 10.1002/fld.4229

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      We present a numerical algorithm to get the approximate solution of time-dependent convection–diffusion–reaction problems, especially in the case of small diffusion. The numerical method is based on fractional-step θ-scheme in time combined with bubble-based finite element methods in space. We further compare the proposed algorithm with two different stabilized methods on several benchmark problems. Numerical experiments illustrate the good performance of the proposed method even on coarse meshes as compared with the others.

    4. A spectral boundary integral method for inviscid water waves in a finite domain

      Jeong-Sook Im and John Billingham

      Version of Record online: 7 MAR 2016 | DOI: 10.1002/fld.4225

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      In this paper, we show how the spectral formulation of Baker, Meiron and Orszag can be used to solve for waves on water of infinite depth confined between two flat, vertical walls and also how it can be modified to take into account water of finite depth with a spatially varying bottom, in each case using Chebyshev polynomials as the basis for the solution.

    5. Modeling of static contact angles with curved boundaries using a multiphase lattice Boltzmann method with variable density and viscosity ratios

      Sébastien Leclaire, Kamilia Abahri, Rafik Belarbi and Rachid Bennacer

      Version of Record online: 4 MAR 2016 | DOI: 10.1002/fld.4226

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      A numerical approach for modeling Young's law for static contact angles in a multiphase lattice Boltzmann method is proposed. The contact angle at the boundaries is imposed in much the same way as Dirichlet boundary conditions are generally imposed. The proposed method is able to retrieve analytical solutions for static contact angles in the case of straight and curved boundaries even when variable density and viscosity ratios between the phases are considered.

    6. A fully conservative high-order upwind multi-moment method using moments in both upwind and downwind cells

      Naoyuki Onodera, Takayuki Aoki and Kensuke Yokoi

      Version of Record online: 3 MAR 2016 | DOI: 10.1002/fld.4228

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      We proposed a new type of CIP-CSL schemes (conservation equation solver based on a multi-moment concept). The figures show numerical results of a scalar transport problem by CSL2, CSL3D, CSL3, and CSL3DL (N = 200 and t = 16). The proposed formulations (CSL3D and CSL3DL) are superior to existing CIP-CSL schemes (such as CSL2 and CSL3).

    7. Advanced numerical method for a thermally induced slug flow: application to a capillary closed loop pulsating heat pipe

      M. Manzoni, M. Mameli, C. de Falco, L. Araneo, S. Filippeschi and M. Marengo

      Version of Record online: 3 MAR 2016 | DOI: 10.1002/fld.4222

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      This work proposes an advanced hybrid lumped parameter code for the simulation of two-phase passive thermal systems named pulsating heat pipes. Even if lumped parameter models are not unusual for such devices, for the first time, transient operative conditions are simulated by removing physical simplified assumptions and embedding phase changes. Advanced numerical technique guaranties stabilization of the model and fast simulations allowing extended sensitivity analysis and device designs. Validation shows very good matching with the actual thermo-physical behaviour of the system.

    8. Dilation-based shock capturing for high-order methods

      David Moro, Ngoc Cuong Nguyen and Jaime Peraire

      Version of Record online: 2 MAR 2016 | DOI: 10.1002/fld.4223

    9. On the stabilization of unphysical pressure oscillations in MPS method simulations

      J. Sanchez-Mondragon

      Version of Record online: 29 FEB 2016 | DOI: 10.1002/fld.4227

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      In this paper, pressure stability through the suppression of high-pressure oscillations in the moving particle semi-implicit (MPS) is presented. To validate the suppression of the high-frequency pressure oscillations, modified MPS methods with and without a removable wall are compared with dam-breaking experiment pressure measurements.

    10. High order numerical simulation of the thermal load on a lobed strut injector for scramjet applications

      Yann Hendrik Simsont and Peter Gerlinger

      Version of Record online: 24 FEB 2016 | DOI: 10.1002/fld.4224

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      The paper investigates the flow field inside and outside a hydrogen stut injector coupled with heat transfer in the solid. Simulations use a fourth order MLP (multi-dimensional limiting process) discretization and an all-Mach number preconditioning. It will be shown that the chosen high order scheme achieves excellent results at low-additional cost.

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