International Journal for Numerical Methods in Fluids

Cover image for Vol. 81 Issue 9

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 - 68
  1. 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.

  2. Research paper presented at 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. Research paper presented at Model Reduction and Inverse Problems and Data Assimilation with Geophysical Application

    1. 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.

  4. 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.

  5. Research paper presented at 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.

  6. 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.

  7. Research paper presented at Model Reduction and Inverse Problems and Data Assimilation with Geophysical Application

    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.

  8. Research paper presented at Model Reduction and Inverse Problems and Data Assimilation with Geophysical Applications

    1. 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.

  9. Research paper presented at Model Reduction and Inverse Problems and Data Assimilation with Geophysical Application

    1. 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.

  10. Research Paper Presented at Model Reduction and Inverse Problems and Data Assimilation with Geophysical Application

    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

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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.

  11. 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.

  12. Research paper presented at Model Reduction and Inverse Problems and Data Assimilation with Geophysical Application

    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.

  13. 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.

  14. Research Paper Presented at Model Reduction and Inverse Problems and Data Assimilation with Geophysical Application

    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.

  15. 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.

  16. 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.

  17. 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.

    11. On linear and nonlinear aspects of dynamic mode decomposition

      A. K. Alekseev, D. A. Bistrian, A. E. Bondarev and I. M. Navon

      Version of Record online: 24 FEB 2016 | DOI: 10.1002/fld.4221

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      We propose a framework for dynamic mode decomposition (DMD) with application of the reduced Schmid operator instead of the classic DMD approach. Instead of storing the total operator matrix, the proposed technique ensures computer memory and computing time (CPU) savings of about several orders of magnitude. We emphasize an excellent behavior of the Schmid operator by considering two numerical experiments: the case of a 2D supersonic underexpanded jet on a plate and the problem of the 2D shallow water equations.

    12. An improved unstructured WENO method for compressible multi-fluids flow

      Hongwei Zheng and Wengeng Zhao

      Version of Record online: 17 FEB 2016 | DOI: 10.1002/fld.4210

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      An improved high-order accurate WENO finite volume method based on unstructured grids for compressible multi-fluids flow is proposed in this paper. The reconstructed coefficients are calculated by analytical form of inverse matrix rather than the numerical inversion. This greatly improved the efficiency and the robustness. Numerical results show that there is no spurious oscillation of velocity and pressure across the interface and high-order accurate result can be achieved.

    13. Development of a hybrid particle-mesh method for two-phase flow simulations

      X. Liu, L. Guo, K. Morita and S. Zhang

      Version of Record online: 15 FEB 2016 | DOI: 10.1002/fld.4220

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      A hybrid particle-mesh method was developed for efficient and accurate simulations of two-phase flows. In this method, the main component of the flows is solved by the constrained interpolated profile/multi-moment method, whereas the interface between two phases is rendered by the finite volume particle method. Two benchmark simulations demonstrated the efficiency and accuracy of the method developed.

    14. A stabilized Nitsche-type extended embedding mesh approach for 3D low- and high-Reynolds-number flows

      B. Schott, S. Shahmiri, R. Kruse and W.A. Wall

      Version of Record online: 11 FEB 2016 | DOI: 10.1002/fld.4218

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      Complex high-Reynolds-number fluid-structure interaction applications require high mesh resolution in the boundary layer region around moving/rotating obstacles. For this purpose, a powerful technique based on the extended finite element method is proposed to embed arbitrary fluid patches into a background fluid discretization using cut elements. Stabilization techniques are provided to guarantee stable and accurate weak imposition of interface coupling conditions based on Nitsche's method independent of the patch location.

  18. Research Article

    1. You have full text access to this OnlineOpen article
      A local mesh refinement approach for large-eddy simulations of turbulent flows

      M. Cevheri, R. McSherry and T. Stoesser

      Version of Record online: 5 FEB 2016 | DOI: 10.1002/fld.4217

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      This paper introduces and validates a local mesh refinement approach for simulations of turbulent flows in complex domains. The method features high-order interpolation schemes at the fine-coarse mesh interfaces and uses up to fourth-order central differencing schemes for convective and diffusive fluxes. It is shown that the local mesh refinement method is able to predict accurately first-order and second-order statistics of two challenging flows, a turbulent channel flow and the flow over a matrix of cubes. The method offers significant savings of computational resources due to the placement of very fine meshes into critical areas, for instance around the cubes, while for the rest of the domain, coarser meshes are employed.

  19. Research Articles

    1. Generation of unstructured curvilinear grids and high-order discontinuous Galerkin discretization applied to a 3D high-lift configuration

      Ralf Hartmann and Tobias Leicht

      Version of Record online: 26 JAN 2016 | DOI: 10.1002/fld.4219

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      This paper includes a description of a complete chain of unstructured curvilinear grid generation and higher order Discontinuous Galerkin flow solution applied to a turbulent flow around a 3D high-lift configuration. A fourth order flow solution of the RANS and k-w turbulence model equations is computed on a fourth order unstructured hybrid (mixed-element) mesh around the 3D high-lift SWING configuration. A highly resolved flow solution is obtained featuring a complex vortex system.

    2. Implicit large eddy simulation using the high-order correction procedure via reconstruction scheme

      Brian C. Vermeire, Siva Nadarajah and Paul G. Tucker

      Version of Record online: 16 JAN 2016 | DOI: 10.1002/fld.4214

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      We perform simulations of turbulent flows using the correction procedure via reconstruction (CPR) scheme. Our results demonstrate that the CPR scheme can be used for implicit large eddy simulation, without the addition of an explicit sub-grid scale model. We find that the high-order schemes are generally more accurate than the low-order schemes on a per degree of freedom basis.

    3. A boundary integral method for computing forces on particles in unsteady Stokes and linear viscoelastic fluids

      H. Feng, A. Córdoba, F. Hernandez, T. Indei, S. Li, X. Li and J. D. Schieber

      Version of Record online: 15 JAN 2016 | DOI: 10.1002/fld.4216

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      We develop an accurate boundary integral method to calculate forces exerted on particles in unsteady Stokes flow and linear viscoelastic fluids. Our numerical method is third-order accurate uniformly in space and corrects the error due to the poles at the axis of symmetry.

    4. Influence of mesh deformation on the quality of large eddy simulations

      Jukka-Pekka Keskinen, Ville Vuorinen, Ossi Kaario and Martti Larmi

      Version of Record online: 11 JAN 2016 | DOI: 10.1002/fld.4215

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      The effect of mesh motion on the outcome of a large eddy simulation was studied in the present article. A turbulent pipe flow (Ret = 360) was used as a test case. The results of this study indicate that runtime mesh deformation can have a noticeable effect on the velocity and energy statistics of a large eddy simulation.

    5. Fluid interface detection technique based on neighborhood particles centroid deviation (NPCD) for particle methods

      Marcio Michiharu Tsukamoto, Liang-Yee Cheng and Fabio Kenji Motezuki

      Version of Record online: 11 JAN 2016 | DOI: 10.1002/fld.4213

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      Particle-based CFD methods are powerful approaches to investigate fluid flows with huge deformations or fragmentation and merging because of their ability of tracking moving interfaces. However, many fluid interface particle detection techniques are simple to implement but with low accuracy or provide relatively good detection results at complicated implementation or higher computational time. Besides a review of the main available techniques, in this paper, a new technique is proposed to improve the accuracy while keeping implementation easy and with low computational cost.

    6. Mesh adaptation for large-eddy simulations in complex geometries

      Pierre Benard, Guillaume Balarac, Vincent Moureau, Cecile Dobrzynski, Ghislain Lartigue and Yves D'Angelo

      Version of Record online: 21 DEC 2015 | DOI: 10.1002/fld.4204

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      This paper presents a novel mesh adaptation strategy in the context of Large Eddy Simulation (LES). Two mesh quality criteria are defined, one for the discretization of the mean field and the other for the turbulent kinetic energy resolution. A parallel mesh adaptation strategy, based on these criteria, is proposed and applied to the simulation of the turbulent iso-thermal flow in a complex meso-scale combustor. It shows a large improvement in the quality of the results with a moderate over-cost.

    7. Fujiwhara interaction of tropical cyclone scale vortices using a weighted residual collocation method

      Raymond P. Walsh and Jahrul M. Alam

      Version of Record online: 21 DEC 2015 | DOI: 10.1002/fld.4209

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      We have investigated a collocation methodology for the numerical simulation of Fujiwhara interactions between cyclone scale vortices. The method is validated by computing the rotational period (t*) of the Fujiwhara interaction, as well as by simulating concentric eyewal patterns and barotropic instability of tropical cyclones. Numerical simulation Fujiwhara interactions at moderately high Reynolds numbers, such as for inline image, show that the kinetic energy of cyclones is consolidated into larger scales with a concurrent enstrophy cascade.

    8. Three-dimensional modeling of non-hydrostatic free-surface flows on unstructured grids

      Xin Liu, Abdolmajid Mohammadian and Julio Ángel Infante Sedano

      Version of Record online: 18 DEC 2015 | DOI: 10.1002/fld.4212

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      A numerical model was presented for the simulation of three-dimensional unsteady non-hydrostatic shallow water flows. A sigma coordinate system with a collocated arrangement of three-dimensional velocity components was used to simulate the variation of water depth during the time steps. The numerical results showed that the model is capable of producing non-oscillatory and accurate results.

    9. Numerical study of the properties of the central moment lattice Boltzmann method

      Yang Ning, Kannan N. Premnath and Dhiraj V. Patil

      Version of Record online: 17 DEC 2015 | DOI: 10.1002/fld.4208

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      A comparative numerical study of the cascaded MRT LBM, which is based on central moments, and the standard MRT LBM, which is based on raw moments, is presented. For example, this figure shows that the streamlines in the cavity flow for Re = 5000 computed using the cascaded LBM is in excellent agreement with those of the standard MRT LBM. Furthermore, substantial improvement in the numerical stability is also achieved with the cascaded LBM.

    10. Pressure-stabilized maximum-entropy methods for incompressible Stokes

      K. Nissen and W. A. Wall

      Version of Record online: 17 DEC 2015 | DOI: 10.1002/fld.4205

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      We present a parameter-free stable maximum-entropy method for incompressible Stokes flow. Stable and stabilized velocity-pressure formulation that already exist for other computational methods are investigated and evaluated in order to develop different approaches towards a stable maximumentropy scheme. The method's excellent performance is shown by results for two analytical tests, including a presentation of the convergence behavior, and for the leaky lid-driven cavity as a typical benchmark problem.

    11. An efficient and energy stable scheme for a phase-field model for the moving contact line problem

      Sebastian Aland and Feng Chen

      Version of Record online: 16 DEC 2015 | DOI: 10.1002/fld.4200

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      In the study of the phase-field model for the moving contact line problem, a linear and energy stable numerical scheme was proposed in the paper for solving the Navier-Stokes-Cahn-Hilliard system subject to a new set of complex boundary conditions. Performance and visualization were provided in the work.

  20. Short Communications

    1. A hybrid time stepping scheme combining explicit Runge–Kutta with implicit LU-SGS for Navier–Stokes equations

      Fengling Lu

      Version of Record online: 15 DEC 2015 | DOI: 10.1002/fld.4211

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      We proposed a combination of explicit Runge–Kutta with implicit LU-SGS scheme at the level of system matrix. The combination makes the discretized governing equations expressed as a compound of explicit and implicit matrix operator. Numerical results show that the convergence rate of the present scheme is almost the same as that of the LU-SGS implicit scheme for the same splitting grid and the same CFL number. In the numerical case, the present scheme saved 50% of the memory resources compared with the fully implicit LU-SGS.

  21. Research Articles

    1. An SPH pressure correction algorithm for multiphase flows with large density ratio

      L. Zhou, Z. W. Cai, Z. Zong and Z. Chen

      Version of Record online: 15 DEC 2015 | DOI: 10.1002/fld.4207

      Thumbnail image of graphical abstract

      In this work, we propose an interfacial pressure correction algorithm for SPH simulation of multiphase flows with large density ratios. This correction algorithm helps to improve the stability of the original model, especially for long-time problems.

    2. A new r-ratio formulation for TVD schemes for vertex-centered FVM on an unstructured mesh

      Zhuo Zhang, Zhi-yao Song, Jun Kong and Di Hu

      Version of Record online: 10 DEC 2015 | DOI: 10.1002/fld.4206

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      This paper presents a new r-ratio formulation for TVD schemes for vertex-centered finite volume method on an unstructured mesh. Through several numerical tests as shown later (concentration along x-axis in test of a spot moving in a rotating flow field), the new formulation has higher accuracy and less oscillations than traditional formulations, while it demonstrates a good adaptability to different unstructured meshes.

    3. A free surface flow solver for complex three-dimensional water impact problems based on the VOF method

      Van-Tu Nguyen and Warn-Gyu Park

      Version of Record online: 9 DEC 2015 | DOI: 10.1002/fld.4203

      Thumbnail image of graphical abstract

      A robust numerical solver based on the pseudo-compressibility Navier–Stokes model and the volume-of-fluid interface tracking method was developed for three-dimensional simulation of complex, free surface, and water impact flows. The proposed method is implemented using a generalized curvilinear coordinate system to facilitate complex, arbitrary simulations of the flows in practical problems. Several example computations concerning the numerical resolution, stability, and important physical characteristics of hydraulic and hydrodynamic problems exhibit a very good agreement with experimental and numerical data published in the literature.

    4. Local maximum principle satisfying high-order non-oscillatory schemes

      Ritesh Kumar Dubey, Biswarup Biswas and Vikas Gupta

      Version of Record online: 9 DEC 2015 | DOI: 10.1002/fld.4202

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      Using a local maximum principle, the solution region of hyperbolic scalar conservation law is classified into sub-regions where at least second-order non-oscillatory approximation can be achieved. Nonlinear stability bounds are given, which ensure for non-occurrence of induced oscillations by second-order schemes. Using these bounds, second-order accurate hybrid numerical schemes are constructed with the help of a shock detector, which can preserve high accuracy at non-sonic extrema without exhibiting any induced local oscillations or clipping error.

    5. Stabilisation of AMG solvers for saddle-point stokes problems

      Ronald Webster

      Version of Record online: 8 DEC 2015 | DOI: 10.1002/fld.4199

      Thumbnail image of graphical abstract

      A method of stabilisation is proposed for fully-implicit, algebraic multi-grid, solutions of saddle-point, coupled-field, problems. Mesh-independent convergence is demonstrated for (A) smoothed-aggregation AMG and (B) classical AMG. The reduction/convergence factors, ρ, are independent of both the mesh resolution, Q, and the degree of coarsening, χ, in the AMG coarse-grid approximations.

    6. An immersed boundary method for unstructured meshes in depth averaged shallow water models

      Pablo Ouro, Luis Cea, Luis Ramírez and Xesús Nogueira

      Version of Record online: 6 DEC 2015 | DOI: 10.1002/fld.4201

      Thumbnail image of graphical abstract

      An immersed boundary method for use on unstructured meshes is proposed, with particular focus on its application to depth averaged shallow water models. Moving least-squares is used to generate the interpolation functions. The method is applied to the flow around a spur dike, a dam break with an isolated obstacle and the flow around an array of obstacles, and results are compared with simulations using classic body fitted meshes and experimental data. Good agreement is found between the numerical methods.

    7. An immersed interface method for flow past circular cylinder in the vicinity of a plane moving wall

      Zhong Li, Rajeev K. Jaiman and Boo Cheong Khoo

      Version of Record online: 6 DEC 2015 | DOI: 10.1002/fld.4198

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      Immersed interface method has been employed to study the shear-free wall proximity effects in the low Reynolds number regime (20≤Re≤200), where the hydrodynamic forces and the critical gap ratio for vortex shedding suppression are investigated. We have found that the mean drag coefficient, CD, increases and peaks at e/D=0.5 with the increase of e/D and keeps decreasing gently from e/D=0.5 to 2.0, while the mean lift coefficient, CL, decreases monotonically with the increase of e/D . With the consistent trends of force coefficients, new correlations have been proposed for the lift and drag coefficients as a function of e/D and Re.

    8. A consistent incompressible SPH method for internal flows with fixed and moving boundaries

      S. Jahangiri Mamouri, R. Fatehi and M. T. Manzari

      Version of Record online: 6 DEC 2015 | DOI: 10.1002/fld.4196

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      A consistent Incompressible smoothed particle hydrodynamics (ISPH) method is presented. The method employs first-order consistent discretization schemes for both the first-order and secondorder spatial derivatives and benefits from a robust boundary condition implementation. It is shown that for the range of two-dimensional incompressible laminar internal flow problems studied in this work, the proposed algorithm is more accurate and computationally more efficient compared with its standard ISPH counterpart.

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