International Journal for Numerical Methods in Fluids

Cover image for Vol. 78 Issue 3

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

Edited By: Rémi Abgrall, Charbel Farhat

Impact Factor: 1.329

ISI Journal Citation Reports © Ranking: 2013: 19/31 (Physics Fluids & Plasmas); 32/95 (Mathematics Interdisciplinary Applications); 58/102 (Computer Science Interdisciplinary Applications); 63/139 (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. Research Articles

    1. Vortex penalization method for bluff body flows

      Chloe Mimeau, Federico Gallizio, Georges-Henri Cottet and Iraj Mortazavi

      Article first published online: 22 APR 2015 | DOI: 10.1002/fld.4038

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      This work presents a hybrid vortex-immersed boundary method in order to handle transitional and highly transitional flows past complex bodies. We highlight in this paper the numerical and practical interests of coupling hybrid particle methods and the penalization technique exposing two different types of applications: the simulation of a rotating turbine blade for a Reynolds number up to 10,000 and the analysis of the flow around a semi-circular cylinder covered with a porous coating for passive flow control issues.

    2. A kernel gradient free (KGF) SPH method

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

      Article first published online: 21 APR 2015 | DOI: 10.1002/fld.4037

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      This paper presents an improved finite particle method (FPM), which only involves kernel function itself in kernel and particle approximation and therefore is a kernel gradient-free (KGF) SPH method. As shown in the figure (vertical velocity profiles along the horizontal centerline for a lid-driven shear cavity problem), KGF-SPH has a comparable accuracy with FPM, which is of higher order accuracy than conventional SPH, while KGF-SPH is more flexible in selecting kernel functions than SPH and FPM.

    3. Practical aspects of p-multigrid discontinuous Galerkin solver for steady and unsteady RANS simulations

      Zhenhua Jiang, Chao Yan, Jian Yu and Wu Yuan

      Article first published online: 21 APR 2015 | DOI: 10.1002/fld.4035

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      Two types of multigrid methods and a multigrid preconditioned Newton–Krylov method are investigated, and both steady and unsteady algorithms are considered. For steady algorithms, a novel CFL scheduling strategy and a modified linear smoothing technique are proposed to enhance robustness and improve efficiency, respectively. For unsteady algorithms, special attention has been paid to the cycling strategy and the full multigrid technique, and we point out a significant difference on the parameter selection for unsteady computations.

  2. Research Article

    1. An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

      D. A. Bistrian and I. M. Navon

      Article first published online: 15 APR 2015 | DOI: 10.1002/fld.4029

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      We propose an improved algorithm for dynamic mode decomposition (DMD) decomposition of 2-D flows originating from meteorology, and we give a new criterion of selecting the optimal Koopman modes. A rigorous error analysis for the reduced order models obtained by the classic proper orthogonal decomposition and the improved DMD is presented, and a quantitative comparison of the spatial modes computed from the two decompositions is performed.

  3. Research Articles

    1. Parallel domain decomposition method for finite element approximation of 3D steady state non-Newtonian fluids

      Wen-Shin Shiu, Feng-Nan Hwang and Xiao-Chuan Cai

      Article first published online: 15 APR 2015 | DOI: 10.1002/fld.4027

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      We introduce a stabilized finite element method for 3D non-Newtonian fluids and a parallel algorithm for solving the large nonlinear system of algebraic equations. The domain decomposition-based preconditioning algorithm is quite effective for these highly ill-conditioned problems with a wide range of physical parameters. Using numerical experiments, we provide some quantitative analysis of certain rotational eccentric annular flows in terms of pressure (left) and shear stress distributions (right) for the pseudoplastic case (top) and the dilatant case (bottom).

    2. A sensitivity analysis on the parameter of the GLS method for a second-gradient theory of incompressible flow

      Antônio G. Barbosa da Cruz, Eduardo G. Dutra do Carmo and Fernando P. Duda

      Article first published online: 14 APR 2015 | DOI: 10.1002/fld.4033

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      Driven-cavity flow problem for a second-gradient fluid with generalized adherence boundary conditions (ϵ = 0.1). The figure shows that the pressure field can be gradually stabilized by using an appropriate Galerkin least square stabilization parameter α. For a small α, oscillations remain in the pressure field. A large value of α, however, leads to over-pressure stabilization which fails to capture the physics of the problem, since the pressure is singular at the top corners.

    3. Stabilized finite element method for flows with multiple reference frames

      L. Pauli, J. W. Both and M. Behr

      Article first published online: 13 APR 2015 | DOI: 10.1002/fld.4032

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      We present a space-time finite element method capable of dealing with flows in multiple co-rotating reference frames. Because equal order interpolation is used for all degrees of freedom, Galerkin/least-squares stabilization is applied. We give a detailed derivation of the equations involved, introduce the variational form, present the stabilization parameters, and also discuss implementation issues. Numerical examples in 2D and 3D show generality and efficiency of the method, if steady-state behavior of rotating components is sufficient for the CFD analysis.

    4. Jacobian-free Newton–Krylov method for implicit time-spectral solution of the compressible Navier-Stokes equations

      Peter J. Attar

      Article first published online: 9 APR 2015 | DOI: 10.1002/fld.4036

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      A Jacobian-free Newton–Krylov method is introduced for the implicit time-spectral solution of the compressible Navier–Stokes equations. A new preconditioner for the Krylov solver (GMRES) is presented, which consists of an approximate factorization of an approximation to the full time-spectral Jacobian. Numerical experiments to characterize the method consist of the simulation of the laminar vortex shedding over a circular cylinder at two post-critical Reynolds numbers.

    5. High-order compact finite difference schemes for the vorticity–divergence representation of the spherical shallow water equations

      Sarmad Ghader and Jan Nordström

      Article first published online: 9 APR 2015 | DOI: 10.1002/fld.4034

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      The super compact finite difference method and the combined compact finite difference method are applied to spatial differencing of the spherical shallow water equations. To advance the solution in time, a semi-implicit Runge–Kutta method is developed and used. The convergence rate for all methods is studied. Assessment of the results shows that the sixth-order and eighth-order combined compactfinite difference method and the sixth-order and eighth-order super compact finite difference methods lead to a remarkable improvement of the solution over the fourth-order compact method.

    6. Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms

      A. Chertock, S. Cui, A. Kurganov and T. Wu

      Article first published online: 9 APR 2015 | DOI: 10.1002/fld.4023

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      We study shallow-water equations with friction terms and develop a semi-discrete central-upwind scheme that is capable of exactly preserving physically relevant steady states and maintaining the positivity of the water depth. The presence of the friction terms increases the complexity of numerical simulations as the underlying semi-discrete system becomes stiff when the water depth is small. We therefore implement an efficient semi-implicit Runge-Kutta time integration method that sustains the well-balanced and sign-preserving properties of the semi-discrete scheme.

    7. A non-iterative implicit algorithm for the solution of advection–diffusion equation on a sphere

      Yuri N. Skiba

      Article first published online: 6 APR 2015 | DOI: 10.1002/fld.4016

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      A balanced implicit and unconditionally stable scheme of second-order approximation is suggested for solving the advection–diffusion equation on a sphere. The finite volume method and splitting algorithm are used for discretizing the problem. The implicit scheme is realized without iterations. The application of method to nonlinear diffusion problems, elliptic problems, and adjoint problems is discussed.

    8. A novel optimization technique for explicit finite-difference schemes with application to AeroAcoustics

      Guilherme Cunha and Stéphane Redonnet

      Article first published online: 6 APR 2015 | DOI: 10.1002/fld.4010

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      In the present paper, we propose an innovative optimization approach for finite difference (FD) schemes, which consists in improving the scheme's formal accuracy through a minimization of its leading-order truncation error. The resulting FD schemes constitute an excellent tradeoff between standard and spectral-like optimized ones, both in terms of (i) accuracy; (ii) robustness; and (iii) numerical efficiency (CPU cost). More precisely, when optimized following that innovative process, any given FD scheme (i) offers a higher accuracy than its standard counterpart whenever the discretization level is marginal (i.e., it behaves as good as a spectral-like optimized one would do), whereas (ii) it presents a better grid convergence behavior than its spectral-like optimized counterpart whenever the mesh grid density is increased (i.e. it behaves as good as a standard scheme would do).

    9. An adaptive multiresolution semi-intrusive scheme for UQ in compressible fluid problems

      R. Abgrall, P. M. Congedo, G. Geraci and G. Iaccarino

      Article first published online: 27 MAR 2015 | DOI: 10.1002/fld.4030

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      We describe and apply a multiresolution strategy into a scheme able to propagate uncertainties in unsteady compressible fluid applications. Reference test cases are performed to demonstrate the convergence properties and the efficiency. The figure shows the evolution of the number of stochastic cells employed for each physical location for the adaptive scheme with and without essentially non-oscillatory reconstruction for a Shock tube problem.

    10. A boundary element method for the solution of finite mobility ratio immiscible displacement in a Hele-Shaw cell

      S. J. Jackson, D. Stevens, H. Power and D. Giddings

      Article first published online: 25 MAR 2015 | DOI: 10.1002/fld.4028

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      The evolution of the fluid interface between two immiscible fluids with a finite mobility ratio is investigated numerically within a Hele-Shaw cell. Simulations in low-mobility ratio regimes typically found in CO2 injection into subsurface aquifers reveal large differences in interfacial patterns compared with those predicted by previous single-phase and high-mobility ratio models. Most significantly, classical finger shielding between competing fingers is inhibited, which can lead to the thinning and breaking of fingers into separate bubbles.

    11. On the approximate zeroth and first-order consistency in the presence of 2-D irregular boundaries in SPH obtained by the virtual boundary particle methods

      Georgios Fourtakas, Renato Vacondio and Benedict D. Rogers

      Article first published online: 25 MAR 2015 | DOI: 10.1002/fld.4026

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      The described solid boundary treatment shows significant improvements for the zeroth and first moments of the kernel over previous virtual boundary particle methods. The pressure and velocity fields show close agreement to analytical values. Particles near the solid wall remained uniformed without unphysical gaps for the static and the dynamic cases examined with improvement over the previous virtual boundary particle methods.

    12. A hybrid implicit scheme for solving Navier–Stokes equations

      Gang Wang, Haris Hameed Mian, Yi Liu and Zhengyin Ye

      Article first published online: 21 MAR 2015 | DOI: 10.1002/fld.4019

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      • A new two-stage hybrid implicit scheme is developed and presented to solve 3D compressible Navier–Stokes equations on a hybrid unstructured mesh.
      • The proposed scheme is computationally efficient than the previously developed techniques.
      • The convergence behavior and performance of the developed hybrid implicit scheme have been investigated by simulating 2D and 3D viscous flows and comparing the predicted results with the experimental data.
    13. High-order implicit Runge–Kutta time integrators for fluid-structure interactions

      Jean-François Cori, Stephane Etienne, Andre Garon and Dominique Pelletier

      Article first published online: 18 MAR 2015 | DOI: 10.1002/fld.4020

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      The efficiency of implicit Runge–Kutta integrators of order up to five is tested for application in the field of fluid-structure interactions. These schemes are used for both media in a fully coupled algorithm. Spatial discretization is obtained through the finite element method. It is shown that these schemes perform well at solving classical fluid-structure problems.

    14. Buoyancy modelling with incompressible SPH for laminar and turbulent flows

      A. Leroy, D. Violeau, M. Ferrand and A. Joly

      Article first published online: 13 MAR 2015 | DOI: 10.1002/fld.4025

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      This work aims to model buoyant, laminar or turbulent flows, using a two-dimensional incompressible smoothed particle hydrodynamics model with accurate wall boundary conditions. Thekϵ turbulence model is used, where buoyancy is modelled through an additional term in the kϵ equations. Several benchmark cases are then proposed including heated Poiseuille flows, differentially heated cavities and a lock-exchange flow. Good agreement is obtained with a finite volume approach using an open-source industrial code.

    15. Stability analysis of a polymer film casting problem

      A. Kallel, E. Hachem, F. Rapetti, Y. Demay and J. F. Agassant

      Article first published online: 11 MAR 2015 | DOI: 10.1002/fld.4024

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      The onset of « Draw resonance » instability is investigated for a polymer film casting process using two different numerical strategies: a front-tracking method coupled with linear stability analysis a direct finite-element simulation in an extended domain including the fluid and the surrounding air. The figure depicts the time-dependent polymer film thickness at take up obtained after a small perturbation using the second numerical strategy. The time period and the exponential envelope of the oscillations allow to estimate the leading eigenvalue, which is very close to the one obtained by the linear stability analysis (first strategy).

    16. A discontinuous Galerkin-based sharp-interface method to simulate three-dimensional compressible two-phase flow

      S. Fechter and C.-D. Munz

      Article first published online: 11 MAR 2015 | DOI: 10.1002/fld.4022

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      We present a numerical method for the simulation of compressible two-phase flows. The capabilities of the numerical method are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock-droplet interaction problem at Mach 3.

    17. Implicit LES of free and wall-bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method

      C. Carton de Wiart, K. Hillewaert, L. Bricteux and G. Winckelmans

      Article first published online: 11 MAR 2015 | DOI: 10.1002/fld.4021

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      In this study, the ability of a DG/SIP solver to perform accurate implicit LES is investigated on canonical flows: decaying HIT at very high Reynolds number and channel flows up to Re = 950. Very encouraging results are obtained, and it is showed that the accuracy of the DGM/ILES approach is similar to a state-of-the-art SGS model implemented in a pseudo-spectral code. The parameters of the ILES approach (flux type and penalty parameter) are also investigated.

    18. Simulation of viscoelastic fluids in a 2D abrupt contraction by spectral element method

      Azadeh Jafari, Nicolas Fiétier and Michel O. Deville

      Article first published online: 4 MAR 2015 | DOI: 10.1002/fld.4012

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      This study presents the vortex structure and numerical instability increase occurring when the level of elasticity is enhanced in inertial flows in planar contraction configuration for FENE-P fluid. The calculations are performed using extended matrix logarithm formulation in the context of spectral elements. This formulation helps to reach higher values of the Weissenberg number when compared with the classical one.

    19. Mass conservation in computational morphodynamics: uniform sediment and infinite availability

      Niels Gjøl Jacobsen

      Article first published online: 2 MAR 2015 | DOI: 10.1002/fld.4015

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      1. A perfectly mass conserving face-to-vertex interpolation scheme for computational morphodynamics on generally unstructured meshes is proposed and tested.
      2. A geometric sand sliding routine is devised and tested for mass conservation.
      3. Analysis of other face-to-vertex interpolation schemes from the literature is conducted to check whether they are mass conserving, and if yes, under which conditions.
      4. Other special topics, such as numerical filtering and morphological acceleration, are considered in the light of the mass conservation.
    20. Numerical simulation of two-dimensional Kelvin–Helmholtz instability using weakly compressible smoothed particle hydrodynamics

      Thomas Yue, Frazer Pearce, Arno Kruisbrink and Herve Morvan

      Article first published online: 27 FEB 2015 | DOI: 10.1002/fld.4017

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      The combined use of a multi-fluid SPH scheme and a viscosity switch accurately resolve the Kelvin Helmholtz Instability between two ideal gases. The effective viscosity of the presented results are strongly dependent on the SPH artificial viscosity parameter, with a linear dependence of 0.15. The utilisation of a viscosity switch significantly reduce the spurious viscosity dependence. The linear growth rate in the results are found to be in satisfactory agreement with analytical expectations, with an average relative error of 13%.

    21. A component framework for the parallel solution of the incompressible Navier–Stokes equations with Radau-IIA methods

      J. Rang and R. Niekamp

      Article first published online: 23 FEB 2015 | DOI: 10.1002/fld.4018

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      In this paper, we consider higher order Radau-IIA methods for the discretization of the incompressible Navier–Stokes equations. The nonlinear systems are solved with a simplified Newton method and transformation of the coefficient matrix such that the arising linear systems can be solved in parallel. Numerical examples show that high order in the pressure component can be achieved and that the proposed solution technique is very effective.


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