International Journal for Numerical Methods in Fluids

Cover image for Vol. 80 Issue 8

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

VIEW

  1. 1 - 55
  1. Research Article

    1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

    12. The intersection marker method for 3D interface tracking of deformable surfaces in finite volumes

      Mark Ho, Guan Yeoh, John Reizes and Victoria Timchenko

      Article first published online: 25 OCT 2015 | DOI: 10.1002/fld.4182

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      The intersection marker method is a novel approach for modelling an arbitrary 3D surface within an array of cubic control volumes. Intersection marker's novelty lies in its ability to remesh the interface on a cell-by-cell basis whilst maintaining surface continuity and local volume conservation without the use of permanent surface markers.

    13. Optimization of the ADER-DG method in GPU applied to linear hyperbolic PDEs

      Cristóbal E. Castro, Jörn Behrens and Christian Pelties

      Article first published online: 25 OCT 2015 | DOI: 10.1002/fld.4179

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      In the figure, we show a convergence test considering the 2D linear elastic wave equation. We compare double precision and single precision of the graphics processor unit implementation against the CPU code SeisSol for different orders from second (P1) to sixth (P5). In the vertical axis, the error level is obtained using the L_2 norm. The figure on the left depicts the error against mesh size, while on the right, the horizontal axis represents computational time.

    14. Unsteady shock-fitting for unstructured grids

      A. Bonfiglioli, R. Paciorri and L. Campoli

      Article first published online: 23 OCT 2015 | DOI: 10.1002/fld.4183

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      An unstructured, shock-fitting algorithm, originally developed to simulate steady flows, has been further developed to make it capable of dealing with unsteady flows. The present paper discusses and analyses the additional features required to extend to unsteady flows the steady algorithm.

    15. Modal decomposition-based global stability analysis for reduced order modeling of 2D and 3D wake flows

      Witold Stankiewicz, Marek Morzyński, Krzysztof Kotecki, Robert Roszak and Michał Nowak

      Article first published online: 23 OCT 2015 | DOI: 10.1002/fld.4181

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      The method for computation of stability modes for two- and three-dimensional flows is presented. The method bases on the Dynamic Mode Decomposition of the data resulting from Direct Numerical Simulation of the flow in the regime close to steady flow. The resulting modes resemble the eigenmodes of global stability analysis and are used to design low dimensional Galerkin models of theflow.

    16. A mass-conservative staggered immersed boundary model for solving the shallow water equations on complex geometries

      Alberto Canestrelli, Aukje Spruyt, Bert Jagers, Rudy Slingerland and Mart Borsboom

      Article first published online: 23 OCT 2015 | DOI: 10.1002/fld.4180

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      An immersed boundary model for shallow water equations based on a staggered alternating direction implicit solver is proposed. The scheme is implicit, and therefore, the time step is not constrained by the Courant–Friedrichs–Lewy condition. The model accurately describes 2D and 3D flow in both straight and curved channels.

    17. A vertex-centered linearity-preserving discretization of diffusion problems on polygonal meshes

      Jiming Wu, Zhiming Gao and Zihuan Dai

      Article first published online: 13 OCT 2015 | DOI: 10.1002/fld.4178

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      The new vertex-centered scheme possesses the three properties: the local conservation, the symmetry and positive definiteness, and the linearity preserving (preserve the linear solution exactly), which is rarely seen in the existing cell-centered or vertex-centered scheme. The coercivity of the scheme is rigorously analyzed on arbitrary mesh size under some weak geometry assumptions. Several numerical tests show that the new scheme has approximately second-order accuracy on general polygonal meshes.

    18. A well-balanced scheme to capture non-explicit steady states in the Euler equations with gravity

      Vivien Desveaux, Markus Zenk, Christophe Berthon and Christian Klingenberg

      Article first published online: 6 OCT 2015 | DOI: 10.1002/fld.4177

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      We present a finite volume scheme to approximate the Euler equations with a gravitational source term based on a relaxation method. A particular attention is paid on the preservation of the hydrostatic steady-state solutions of the system. Moreover, the scheme is also proven to be robust and entropy preserving.

    19. Development of new finite volume schemes on unstructured triangular grid for simulating the gas–liquid two-phase flow

      Wen Zhou, Jie Ouyang, Lin Zhang, Jin Su, Xiaodong Wang and Binxin Yang

      Article first published online: 5 OCT 2015 | DOI: 10.1002/fld.4174

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      This paper develops a new finite volume scheme for solving the level set equation. The new scheme can preserve the mass conservation accurately in level set method.

    20. The non-reflective interface: an innovative forcing technique for computational acoustic hybrid methods

      Stephane Redonnet, David P. Lockard, Mehdi R. Khorrami and Meelan. M. Choudhari

      Article first published online: 5 OCT 2015 | DOI: 10.1002/fld.4173

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      Regarding those hybrid methods in acoustics for which the propagation stage is based on advanced Computational AeroAcoustics (CAA) techniques, the present article introduces an original forcing technique, namely, the Non-Reflective Interface (NRI), to enable the transfer of an acoustic signal from an a priori noise generation stage into a CAA-based acoustic propagation phase. Unlike most existing forcing techniques, the NRI makes the associated CAA-based hybrid approach compatible with a large variety of realistic noise problems.

    21. A new numerical model for simulations of wave transformation, breaking and long-shore currents in complex coastal regions

      F. Gallerano, G. Cannata and F. Lasaponara

      Article first published online: 2 OCT 2015 | DOI: 10.1002/fld.4164

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      In this paper, we propose a model based on a new contravariant integral form of fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and near shore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. We propose an original shock-capturing scheme, for the numerical integration of the fully nonlinear Boussinesq equation, which is based on a genuinely two-dimensional weighted essentially non-oscillatory reconstruction procedure. It has been demonstrated that the presented Boussinesq model can be used for the simulation of wave fields and nearshore currents in the coastal region characterized by morphologically complex coastal lines and irregular seabeds and by the presence of maritime infrastructures.

    22. Wall-based reduced-order modelling

      Davide Lasagna and Owen R. Tutty

      Article first published online: 1 OCT 2015 | DOI: 10.1002/fld.4163

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      A novel approach for model order reduction for incompressible fluid flows is discussed. A compact set of elementary ‘wall basis functions’ is first derived via POD to provide a low-order representation of the spatial distribution of the surface stresses. A dynamical model, providing the temporal dynamics of the amplitudes of the wall structures, is then identified from data. The method is applied to the paradigmatic example of modelling the flow past a circular cylinder at Re = 200.

    23. A simple finite element method for Stokes flows with surface tension using unfitted meshes

      H. Ji and Q. Zhang

      Article first published online: 30 SEP 2015 | DOI: 10.1002/fld.4176

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      For the static three-dimensional bubble, the proposed method reduces the oscillations near the interface substantially. Note that coefficient matrix of the resulting system of the proposed method is the same as that of the traditional FEM.

    24. L2Roe: a low dissipation version of Roe's approximate Riemann solver for low Mach numbers

      K. Oßwald, A. Siegmund, P. Birken, V. Hannemann and A. Meister

      Article first published online: 24 SEP 2015 | DOI: 10.1002/fld.4175

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      A modification of the Roe scheme is discussed that improves the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is performed by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime, both of the new method L2Roe and the two other methods previously suggested by other authors.

    25. Evaluation of the deflated preconditioned CG method to solve bubbly and porous media flow problems on GPU and CPU

      R. Gupta, D. Lukarski, M. B. van Gijzen and C. Vuik

      Article first published online: 24 SEP 2015 | DOI: 10.1002/fld.4170

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      In this work, we present the implementation of the deflated preconditioned conjugate gradient method on the GPU using PARALUTION. Through our experiments with two different problems, we prove that it is advantageous to use this method in comparison with optimized CPU implementations of preconditioned CG methods.

    26. An efficient WENO limiter for discontinuous Galerkin transport scheme on the cubed sphere

      Wei Guo, Ramachandran D. Nair and Xinghui Zhong

      Article first published online: 23 SEP 2015 | DOI: 10.1002/fld.4171

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      A simple and efficient limiter based on the weighted essentially non-oscillatory methodology is incorporated in the discontinuous Galerkin transport framework on the cubed sphere, with the following distinctive features: high-order accurate, good non-oscillatory properties, easy to implement, and can avoid ghost cells when applied to a corner cell of the cubed sphere.

    27. A parallel monolithic algorithm for the numerical simulation of large-scale fluid structure interaction problems

      Ali Eken and Mehmet Sahin

      Article first published online: 23 SEP 2015 | DOI: 10.1002/fld.4169

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      A novel FSI algorithm is proposed for the large-scale simulation of fluid-structure interaction problems in a fully coupled form. A special attention is given to satisfy both the local and global discrete geometric conservation law (DGCL) in order to conserve the total fluid volume/mass in machine precision. Large-scale numerical results are presented for several classical FSI benchmark problems.

    28. Accurate and consistent particle tracking on unstructured grids

      G. S. Ketefian, E. S. Gross and G. S. Stelling

      Article first published online: 23 SEP 2015 | DOI: 10.1002/fld.4168

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      We present a new 2-D Lagrangian particle-tracking method on triangular unstructured grids that is more accurate than previously published methods and does not suffer from unphysical particle clustering. We also present the complete analytic solution to the 2-D system of ordinary differential equations (ODEs) governing particle tracks, the analytic solution to the linear system of locally mass-conserving constraints used to obtain the coefficients in the ODEs, and numerical tests demonstrating the accuracy and mass-conserving property of the method.

    29. An efficient semi-implicit subgrid method for free-surface flows on hierarchical grids

      F. W. Platzek, G. S. Stelling, J. A. Jankowski, R. Patzwahl and J. D. Pietrzak

      Article first published online: 22 SEP 2015 | DOI: 10.1002/fld.4172

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      We present a semi-implicit method for free surface flows that incorporates high-resolution geometric data on subgrid level and applies a hierarchical grid solution strategy. The subgrid method makes sure that coarse-grid solutions within the hierarchical grid approach resemble the fine-grid solution, thereby considerably improving the efficiency and accuracy of the hydrodynamic model and providing automatic insight in grid convergence. A novel interpolation method that avoids the introduction of disturbances was applied to transfer data from coarse to fine grids.

    30. Roe-type Riemann solver for gas–liquid flows using drift-flux model with an approximate form of the Jacobian matrix

      Christiano Garcia da Silva Santim and Eugênio Spanó Rosa

      Article first published online: 22 SEP 2015 | DOI: 10.1002/fld.4165

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    31. A study of reduced-order 4DVAR with a finite element shallow water model

      M. U. Altaf, M. Ambrozic, M. F. McCabe and I. Hoteit

      Article first published online: 16 SEP 2015 | DOI: 10.1002/fld.4167

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      Four-dimensional variational data assimilation is frequently used to improve model forecasting skills. The method although requires computation of the gradient of the cost function, which requires huge programming burden to build the adjoint model. Here, comparative performance analysis on a nonlinear finite element shallow water model is performed using alternate four-dimensional variational data assimilation methodologies based on proper orthogonal decomposition. These approaches are nonintrusive in nature and do not require any modifications to system code; thus, they are very easy to implement.

    32. Assessment of global linear stability analysis using a time-stepping approach for compressible flows

      Y. Ohmichi and K. Suzuki

      Article first published online: 10 SEP 2015 | DOI: 10.1002/fld.4166

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      A set of numerical techniques for global linear stability analysis of compressible flows is developed and assessed. We demonstrated that the proposed method can accurately analyze the global stability of low and high subsonic Mach number flows and be performed with low memory consumption. Numerical experiments show that the outflow boundary causes spurious unstable modes and the radiation and outflow boundary condition and the extension of the computational domain with grid stretching keep the spurious unstable modes to a minimum.

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