International Journal for Numerical Methods in Fluids

Cover image for Vol. 81 Issue 4

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

Edited By: Charbel Farhat, Wolfgang A. Wall

Impact Factor: 1.244

ISI Journal Citation Reports © Ranking: 2014: 18/31 (Physics Fluids & Plasmas); 40/99 (Mathematics Interdisciplinary Applications); 63/102 (Computer Science Interdisciplinary Applications); 73/137 (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 - 56
  1. Research Articles

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

      Tatiana Dobroserdova, Maxim Olshanskii and Sergey Simakov

      Article first published 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.

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

      Dongxin Pan, Chengwen Zhong, Ji Li and Congshan Zhuo

      Article first published 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.

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

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

      Article first published 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.

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

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

      Article first published 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.

    5. 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

      Article first published 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.

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

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

      Article first published 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.

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

      Xianyang Zeng, Min Xiao and Guoxi Ni

      Article first published 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.

  2. Review Articles

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

      Zhenzhen Wang, Gang Li and Olivier Delestre

      Article first published 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.

  3. 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published online: 2 MAR 2016 | DOI: 10.1002/fld.4223

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

      J. Sanchez-Mondragon

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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.

  4. 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

      Article first published 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.

  5. 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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

      Article first published 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. Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

      Mária Lukáčová - Medvid'ová, Hirofumi Notsu and Bangwei She

      Article first published online: 17 DEC 2015 | DOI: 10.1002/fld.4195

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      We propose new energy dissipative characteristic schemes for the diffusive Oldroyd-B equations, which are based either on the finite element or finite difference discretization. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined.

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

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

      Article first published 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.

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

      K. Nissen and W. A. Wall

      Article first published 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.

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

      Sebastian Aland and Feng Chen

      Article first published 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.

  6. Short Communications

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

      Fengling Lu

      Article first published 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.

  7. 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

      Article first published online: 15 DEC 2015 | DOI: 10.1002/fld.4207

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      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 stabilization for three-dimensional discontinuous Galerkin discretizations applied to nonhydrostatic atmospheric simulations

      Sébastien Blaise, Jonathan Lambrechts and Eric Deleersnijder

      Article first published online: 15 DEC 2015 | DOI: 10.1002/fld.4197

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      A stabilization, based upon a reduced-order discretization of the gravity term, ensures the balance between pressure and gravity effects. Validation with a stability analysis and numerical experiments confirming the correct convergence rate.

    3. Deconvolution-based nonlinear filtering for incompressible flows at moderately large Reynolds numbers

      L. Bertagna, A. Quaini and A. Veneziani

      Article first published online: 14 DEC 2015 | DOI: 10.1002/fld.4192

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      We adopt a Leray model for the simulation of fluid flows at moderately high Reynolds numbers and provide directions for tuning the parameters involved in the model. For the implementation, we consider a three-step algorithm that we reformulate as an operator-splitting method. For the first time, this method is applied to a realistic problem of practical interest (flow in a nozzle). We carry out a successful validation against experimental measurements.

    4. 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

      Article first published 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.

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

      Van-Tu Nguyen and Warn-Gyu Park

      Article first published online: 9 DEC 2015 | DOI: 10.1002/fld.4203

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      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.

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

      Ritesh Kumar Dubey, Biswarup Biswas and Vikas Gupta

      Article first published 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.

    7. A high-order discontinuous Galerkin solver for low Mach number flows

      B. Klein, B. Müller, F. Kummer and M. Oberlack

      Article first published online: 9 DEC 2015 | DOI: 10.1002/fld.4193

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      We present a high-order discontinuous Galerkin method for simulating variable density flows at low Mach numbers. The solver is based on the lowMach number equations, which are an approximation of the compressible Navier–Stokes equations in the limit of zero Mach number. Numerical tests for Couette flow with a vertical temperature gradient and natural convection in enclosed cavities confirm the high accuracy of the method.

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

      Ronald Webster

      Article first published online: 8 DEC 2015 | DOI: 10.1002/fld.4199

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      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.

  8. Short Communications

    1. A new smoothness indicator for third-order WENO scheme

      Xiaoshuai Wu, Jianhan Liang and Yuxin Zhao

      Article first published online: 8 DEC 2015 | DOI: 10.1002/fld.4194

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      A new reference smoothness indicator τNP is devised for the third-order weighted essentially non-oscillatory-NP3 scheme to recover its design-order convergence at critical points, by considering the nonlinear combination of the candidate and global smoothness indicators. The good matching between the numerical solutions of weighted essentially non-oscillatory-NP3 and third-order upwind scheme in solving the smooth extremum problem forcefully confirmed the recovery of design-order accuracy. Meanwhile, standard tests also verified the benefit of τNP in producing sharper representation of the discontinuity.

  9. Research Articles

    1. Space-time NURBS-enhanced finite elements for free-surface flows in 2D

      A. Stavrev, P. Knechtges, S. Elgeti and A. Huerta

      Article first published online: 8 DEC 2015 | DOI: 10.1002/fld.4189

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      The paper at hand discusses the application of the recently proposed NURBS-enhanced finite element method (NEFEM) to free-surface flow simulations. In this context the 2D spatial NEFEM formulation is extended into the framework of space-time methods and a suitable kinematic rule for the NURBS motion in time is derived. The performance of the space-time NEFEM is compared to the standard FEM and the ability to preserve mass conservation over time is confirmed.

    2. Edge-based reconstruction schemes for unstructured tetrahedral meshes

      Ilya Abalakin, Pavel Bakhvalov and Tatiana Kozubskaya

      Article first published online: 8 DEC 2015 | DOI: 10.1002/fld.4187

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      The paper considers edge-based reconstruction (EBR) schemes for solving the Euler equations on unstructured tetrahedral meshes. These are vertex-centered schemes for the point-wise values that exploit a high-accuracy quasi-one-dimensional reconstruction of variables on an extended stencil along the edge-based direction. We prove the high accuracy of EBR schemes for uniform grid-like meshes, introduce their economical implementation, and compare them with the polynomial-based finite-volume schemes and flux corrector method.

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

      Pablo Ouro, Luis Cea, Luis Ramírez and Xesús Nogueira

      Article first published online: 6 DEC 2015 | DOI: 10.1002/fld.4201

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      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.

    4. 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

      Article first published 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.

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

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

      Article first published 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.

    6. An improved KGF-SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows

      C. Huang, J. M. Lei, M. B. Liu and X. Y. Peng

      Article first published online: 3 DEC 2015 | DOI: 10.1002/fld.4191

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      In this paper, an improved kernel gradient free (KGF)-smoothed particle hydrodynamics (SPH) method with a novel discrete scheme of Laplacian operator is presented for modeling viscous, incompressible fluid flows. Improved KGF-SPH method avoids nested approximation of first-order derivatives, and keeps the good feature of ‘KGF’. The 2D incompressible flows of lid-driven shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, original and improved KGF-SPH. As shown in the figure (pressure coefficient profiles along upper wall for a lid-driven shear cavity problem), improved KGF-SPH with the novel discrete scheme of Laplacian operator is more accurate and stable than SPH, FPM and original KGF-SPH.

    7. A Q2Q1 integrated finite element method with the semi-implicit consistent CSF for solving incompressible two-phase flows with surface tension effect

      Sanghun Choi, Myung Hwan Cho, Hyoung Gwon Choi and Jung Yul Yoo

      Article first published online: 3 DEC 2015 | DOI: 10.1002/fld.4185

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      In finite element method, a consistent continuum surface force model is introduced by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi-implicit manner to improve temporal stability with an increased time step. The Q2Q1 integrated FEM coupled with the semi-implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability.

    8. An embedded approach for immiscible multi-fluid problems

      P. B. Ryzhakov and A. Jarauta

      Article first published online: 30 NOV 2015 | DOI: 10.1002/fld.4190

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      Gas-liquid systems can be efficiently modeled in a partitioned embedded fashion adopting fixed mesh (Eulerian) approach for the gas and mesh-moving one (Lagrangian) for the liquid. The interface tracking and flow variables' discontinuity across the interface becomes thus a natural feature of the method. Surface tension is applied on the mesh-defined boundary of the liquid phase. The main strength of the approach is the full control over the coupling strength between the sub-domains, allowing for both weak and fully coupled algorithms.

    9. Numerical modeling of wave interactions with coastal structures by a constrained interpolation profile/immersed boundary method

      Xizeng Zhao, Yangyang Gao, Feifeng Cao and Xinggang Wang

      Article first published online: 26 NOV 2015 | DOI: 10.1002/fld.4184

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      Numerical simulations of water wave interaction with coastal structures are performed by an improved CIP-based Cartesian grid method, in which a more accurate interface capturing scheme is combined for the free surface capturing and the immersed boundary method for the solid boundary treatment. Computations are compared with available analytical, experimental and other numerical results. The present model proves to be a promising tool for simulation of coastal engineering applications with acceptable accuracy.

    10. A mass-conserving level-set method for simulation of multiphase flow in geometrically complicated domains

      F. Raees, D. R. van der Heul and C. Vuik

      Article first published online: 8 NOV 2015 | DOI: 10.1002/fld.4188

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      We present the extension of the MCLS method toward unstructured triangular grids for two phase flow. The VoF function and the inverse function derived for a triangular mesh are very simple, robust and efficient to evaluate. Our approach is significantly more efficient and robust than the original MCLS formulation. Numerical experiments indicate the LS field converges with second order accuracy in space and mass is conserved up to machine precision.

    11. Developing a hybrid flux function suitable for hypersonic flow simulation with high-order methods

      Dongfang Wang, Xiaogang Deng, Guangxue Wang and Yidao Dong

      Article first published online: 8 NOV 2015 | DOI: 10.1002/fld.4186

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      In this paper, we develop a very robust hybrid flux function to overcome the shock instability in hypersonic flow simulation with high-order methods. Multidimensional dissipation and entropy correction based on local flow field are introduced to enhance the robustness and resolution of the hybrid flux function. A series of tests shows that this new hybrid flux function with a fifth-order weighted compact nonlinear scheme (WCNS) is not only robust for shock-capturing but also accurate for hypersonic heat transfer prediction.

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