International Journal for Numerical Methods in Fluids

Cover image for Vol. 83 Issue 1

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 - 54
  1. Research Articles

    1. Numerical analysis of conservative unstructured discretisations for low Mach flows

      J. Ventosa-Molina, J. Chiva, O. Lehmkuhl, J. Muela, C. D. Pérez-Segarra and A. Oliva

      Version of Record online: 1 DEC 2016 | DOI: 10.1002/fld.4350

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      In the paper finite-volume collocated and unstructured discretizations to simulate Low Mach flows are analyzed. The collocated method is shown to be more computationally efficient. Furthermore, a Symmetry-Preserving and Upwinding numerical schemes for face interpolations are studied, focusing on their behavior on unstructured meshes. Tests cases include non-reactive and chemically reactive simulations.

    2. Role of the momentum interpolation mechanism of the Roe scheme in shock instability

      Xiao-dong Ren, Chun-wei Gu and Xue-song Li

      Version of Record online: 29 NOV 2016 | DOI: 10.1002/fld.4351

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      1. The inherent momentum interpolation method (MIM) of the Roe scheme plays the most important role in the shock instability phenomenon.
      2. Unexpected MIM is activated on the cell faces nearly parallel to high-Mach-number flows and low-Mach-number cells in numerical shock.
      3. An improved Roe scheme is proposed, which consider the requirement of MIM for incompressible and compressible flows, and can achieve the aim of decreasing numerical dissipation to cure shock instability.
    3. An ALE approach to mechano-chemical processes in fluid–structure interactions

      Yifan Yang, Thomas Richter, Willi Jäger and Maria Neuss-Radu

      Version of Record online: 16 NOV 2016 | DOI: 10.1002/fld.4345

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      In this paper, we formulate a mechano-chemical fluid–structure interaction problem. A plaque formation model is chosen as a proof of concept scenario. The ALE method is chosen to solve the system numerically and delivers very reliable results.

    4. A new mesh relaxation approach and automatic time-step control method for boundary integral simulations of a viscous drop

      I. R. Siqueira, R. B. Rebouças, T. F. Oliveira and F. R. Cunha

      Version of Record online: 16 NOV 2016 | DOI: 10.1002/fld.4346

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      A mesh relaxation method which completely removes the Lagrangian behavior of the Boundary Integral mesh was developed, allowing long-term simulations without significant mesh distortion, even for high viscosity ratio drops. The dependence of the mesh on the flowŠs history was monitored by computing the standard deviation of the elements areas along the simulations. An automatic time-step control method, based on the Drop Cauchy-Green tensor was created to accelerate time evolution and save computational time, without loss of accuracy.

    5. Finite element methods for a class of continuum models for immiscible flows with moving contact lines

      Arnold Reusken, Xianmin Xu and Liang Zhang

      Version of Record online: 15 NOV 2016 | DOI: 10.1002/fld.4349

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      We present a level-set based finite element method for two-phase incompressible flows with moving contact lines. We use a sharp interface model and consider a class of continuum models for describing the moving contact lines. A general variational formulation and a corresponding energy estimate are derived. The discontinuous pressure is accurately approximated by using a stabilized extended finite element space, and a Nitsche technique is applied to weakly impose the Navier boundary conditions.

  2. Research Paper Presented at MULTIMAT 2015

    1. Optimal control for reinitialization in finite element level set methods

      Christopher Basting, Dmitri Kuzmin and John N. Shadid

      Version of Record online: 14 NOV 2016 | DOI: 10.1002/fld.4348

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      A new reinitialization technique based on an optimal control approach is presented. The residual of the Eikonal equation is incorporated into the objective functional. The state equation is given by the level set transport equation but augmented by an additional source term. The method is evaluated numerically in three different examples and compared to other PDE-based reinitialization techniques.

  3. Research Articles

    1. An accurate pressure–velocity decoupling technique for semi-implicit rotational projection methods

      Ehsan Tavakoli

      Version of Record online: 10 NOV 2016 | DOI: 10.1002/fld.4347

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      Herein, we propose an accurate technique to decouple pressure from the momentum equation by incorporating the principle form of the pressure Poisson equation for semi-implicit projection methods. The velocity correction step is redefined, and boundary conditions are introduced accordingly. It is shown that the present method can preserve the order of accuracy for second-order and high-order finite difference simulations. A very good agreement is observed between the results of the present method and the benchmark simulations.

    2. Projection-based variational multiscale method for incompressible Navier–Stokes equations in time-dependent domains

      Birupaksha Pal and Sashikumaar Ganesan

      Version of Record online: 9 NOV 2016 | DOI: 10.1002/fld.4338

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      A projection-based variational multiscale method for computations of incompressible Navier–Stokes equations in time-dependent domains is presented. An arbitrary Lagrangian–Eulerian approach with an elastic mesh moving technique with mesh-dependent stiffness is tailored with the variational multiscale method to handle moving boundaries. Simulations of flow around a static beam attached to a square base, around an oscillating beam, and around a plunging aerofoil are presented.

  4. Research Paper Presented at MULTIMAT 2015

    1. An efficient high order direct ALE ADER finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics

      Walter Boscheri

      Version of Record online: 3 NOV 2016 | DOI: 10.1002/fld.4342

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      The arbitrary-Lagrangian-Eulerian ADER MOOD quadrature-free algorithm is a finite volume scheme that achieves high order of accuracy in space by limiting the reconstruction relying on the a posteriori MOOD strategy and reaches the same order of accuracy in time using the ADER approach. Efficiency is furthermore improved by a quadrature-free integration of the numerical fluxes. Hydrodynamics and magnetohydrodynamics equations are considered in multiple space dimensions on unstructured meshes in 2D and in 3D, and the speedup is monitored.

  5. Research Articles

    1. Acoustic simulation using a novel approach for reducing dispersion error

      G. Wang, X.Y. Cui and G.Y. Li

      Version of Record online: 20 OCT 2016 | DOI: 10.1002/fld.4339

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      A novel approach that combines Shepard interpolation and linear shape functions is proposed for reducing the dispersion error in acoustic analysis. For each independent element, the gradient field is formed based on the element itself and its adjacent elements sharing common edges (or faces). Theoretic analysis and numerical results illustrate that the present algorithm performs well in simulating high wavenumber problems.

    2. A robust low-dissipation AUSM-family scheme for numerical shock stability on unstructured grids

      Fan Zhang, Jun Liu, Biaosong Chen and Wanxie Zhong

      Version of Record online: 19 OCT 2016 | DOI: 10.1002/fld.4341

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      A hybrid upwind scheme is devised for improving the shock stability of SLAU scheme. The dissipation term of SLAU flux function is modified to give a new hybrid flux function. The hybrid flux function is used on the solution of momentum fluxes. In the test cases, the hybrid scheme is showing improvements on the numerical shock stability.

    3. Dissipation matrix and artificial heat conduction for Godunov-type schemes of compressible fluid flows

      Jiequan Li, Baolin Tian and Shuanghu Wang

      Version of Record online: 19 OCT 2016 | DOI: 10.1002/fld.4340

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      This paper aims to reassess the Riemann solver for compressible fluid flows in the Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov-type schemes in the Lagrangian frame, which connects to some numerical defects such as the wall-heating phenomenon and start-up errors. To cure the defects, the artificial heat conduction, in addition to the traditional numerical viscosity, is introduced via a passage of the Lax–Friedrichs type discretization of internal energy.

    4. A robust flux splitting method with low dissipation for all-speed flows

      Di Sun, Chao Yan, Feng Qu and Ruofan Du

      Version of Record online: 12 OCT 2016 | DOI: 10.1002/fld.4337

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      We propose a robust flux splitting method with low dissipation for all speed flows. A low-dissipation modification is properly applied to the convection and the pressure parts of the inviscid terms of the Euler equation, respectively, which improves the accuracy obviously without enhancing the computational costs of the method. The results of this study prove that the new method can enhance the accuracy and robustness for solving all-speed flows.

    5. Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS-LES models for predicting flow fields with separation and reattachment

      G. Kumar, S. K. Lakshmanan, H. Gopalan and A. De

      Version of Record online: 4 OCT 2016 | DOI: 10.1002/fld.4334

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      In this study, a generic non-linear blended modeling framework for performing hybrid RANS-LES simulations is proposed and flow over the periodic hills is used as the test case for model evaluation. Analysis of the simulations suggests that the non-linear closures are less sensitive to the RANS-LES coupling method and grid resolution. Also, good agreement has been found for flow statistics compared with the existing experimental data for simulations performed using NSST-Blended at higher Reynolds number.

    6. A mixed-interpolation finite element method for incompressible thermal flows of electrically conducting fluids

      Haruhiko Kohno

      Version of Record online: 4 OCT 2016 | DOI: 10.1002/fld.4292

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      A high-speed finite element scheme is proposed for simulation of incompressible MHD flows with convective heat transfer. In the proposed scheme, Q2-Q1 elements are used for the interpolations of the velocity, pressure, and temperature, while the electric field and magnetic flux density are interpolated using vector shape functions in the subdivided four-node elements. The robustness of the scheme is investigated using highly distorted meshes in well-known problems, and the results showing the improvement of calculation speed are also presented.

    7. Managing false diffusion during second-order upwind simulations of liquid micromixing

      Robert T. Bailey

      Version of Record online: 4 OCT 2016 | DOI: 10.1002/fld.4335

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      Numerical simulations were conducted to determine an ‘effective’ false diffusion coefficient (Dfalse) for the second-order upwind finite volume method. Expressions for estimating the spacing required to reduce Dfalse to some desired (low) level were incorporated into a procedure for managing false diffusion when simulating steady, liquid micromixing using structured and unstructured meshes.

  6. Research Paper Presented at MULTIMAT 2015

    1. A 3D finite volume scheme for solving the updated Lagrangian form of hyperelasticity

      G. Georges, J. Breil and P.-H. Maire

      Version of Record online: 29 SEP 2016 | DOI: 10.1002/fld.4336

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      This paper presents the 3D extension of the EUCCLHYD scheme (Explicit Unstructured Cell-Centered Lagrangian HYDrodynamics) [Maire SIAM 2007] for the numerical modeling of the hyperelasticity system at first order in space and time. The constitutive law is derived by means of a Coleman–Noll procedure in the case of isotropic neo-Hookean materials. The scheme is validated on three test cases and is proved to have an inherent 3D nature when shearing is present such as in the oscillating beam problem (refer to Figure 1).

  7. 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.

    5. 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.

    6. 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.

    7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.
  19. 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.

  20. 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.

  21. 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.

  22. 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.

  23. 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.

  24. 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

      Thumbnail image of graphical abstract

      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.

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

    1. 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

      Thumbnail image of graphical abstract

      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.

  26. 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

      Thumbnail image of graphical abstract

      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.

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