A simple parameter-free entropy correction for approximate Riemann solvers

Helluy, Philippe; Hérard, Jean-Marc; Mathis, Hélène; Müller, Siegfried

doi:10.1016/j.crme.2010.07.007

Cited by 14 publications

(11 citation statements)

References 13 publications

(22 reference statements)

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“…We check at once that formulae (18), (19), (20) are the unique solutions of (22), (23), (24). Eventually, the constructed analytical solution to the Riemann problem associated with (9) and initial conditions (14) can be sketched as:…”

Section: Analytical Solution Of the Riemann Problemmentioning

confidence: 99%

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A relaxation scheme for hybrid modelling of gas-particle flows

Dorogan¹,

Guingo²,

Hérard³

et al. 2012

Computers & Fluids

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International audienceThis paper aims at proposing a relaxation scheme that allows to obtain stable approximations for a system of partial differential equations which governs the evolution of the void fraction and the mean velocity in the particle phase of two-phase flows. This system involves the divergence of a particle kinetic tensor, which is provided by a Lagrangian code and whose components are not smooth. The simulation algorithm is based on the combined use of upwinding and relaxation techniques. The main properties of the method are given, together with the Finite Volume Godunov scheme and this approach is compared to an analogous one that was developed earlier. Some measured rates of convergence in L 1-norm are provided, for a particular choice of the kinetic tensor. To complete the picture, we present some numerical results obtained when non-smooth external data are provided to the system

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Section: Analytical Solution Of the Riemann Problemmentioning

confidence: 99%

“…In this case, the 1-rarefaction wave contains a sonic point. The VFRoe-ncv scheme used in approach (A1) requires an entropy correction at sonic points [24]; otherwise a wrong shock wave develops. On the other hand, the relaxation scheme (A2) exhibits the correct behaviour in the rarefaction wave without any entropy correction.…”

Section: Supersonic Shock Tubementioning

confidence: 99%

A relaxation scheme for hybrid modelling of gas-particle flows

Dorogan¹,

Guingo²,

Hérard³

et al. 2012

Computers & Fluids

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“…One drawback is that it causes the apparition of non-entropic shocks when the left and right eigenvalues (λ L ) and (λ R ) change of sign. To overcome this problem, we consider an entropy correction described in [2]. The previously defined numerical flux is replaced by…”

Section: Entropy Fixmentioning

confidence: 99%

“…We have implemented two differents fluxes for solving the problem: the Rusavov flux, the VFRoe flux [2].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation for the MHD system in 2D using OpenCL

Massaro

Helluy

Loechner³

2014

ESAIM: ProcS

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Abstract. In this work we compute the MHD equations with divergence cleaning on GPU. The method is based on the finite volume approach and Strang dimensional splitting. The simplicity of the approach makes it a good candidate for a GPU implementation with OpenCL. With adequate memory optimization access, we achieve very high speedups, compared to a classical sequential implementation.Résumé. Dans ce travail, nous résolvons les équations de la MHD avec correction de divergence sur carte graphique. La méthode est basée sur les volumes finis et le splitting directionnel de Strang. La simplicité de l'algorithme en fait un bon candidat pour la programmation sur carte graphique sous OpenCL. Avec de bonnes optimisations des accès mémoire, nous obtenons de très bonnes accélérations, comparé à une programmation séquentielle classique.

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“…The VFRoe ncv scheme without entropy correction can approach incorrect rarefaction waves crossing the interface x = 0 and thus authorizes in these points non physical shocks. To solve this problem, we use the following entropy correction presented in [7]:…”

Section: Ale Velocitymentioning

confidence: 99%

A coupled well-balanced and random sampling scheme for computing bubble oscillations

Helluy

Jung

2012

ESAIM: Proc.

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Abstract. We propose a finite volume scheme to study the oscillations of a spherical bubble of gas in a liquid phase. Spherical symmetry implies a geometric source term in the Euler equations. Our scheme satisfies the well-balanced property. It is based on the VFRoe approach. In order to avoid spurious pressure oscillations, the well-balanced approach is coupled with an ALE (Arbitrary Lagrangian Eulerian) technique at the interface and a random sampling remap.Résumé. Nous proposons un schéma de volumes finis pourétudier les oscillations d'une bulle sphérique de gaz dans l'eau. La symétrie sphérique fait apparaitre un terme source géométrique dans leséquations d'Euler. Notre schéma est basé sur une approche VFRoe et préserve lesétats stationnaires. Pouréviter les oscillations de pression, l'approche well-balanced est couplée avec une approche ALE (Arbitrary Lagrangian Eulerian), et uneétape de projection basée sur unéchantillonage aléatoire.

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A simple parameter-free entropy correction for approximate Riemann solvers

Cited by 14 publications

References 13 publications

A relaxation scheme for hybrid modelling of gas-particle flows

A relaxation scheme for hybrid modelling of gas-particle flows

Numerical simulation for the MHD system in 2D using OpenCL

A coupled well-balanced and random sampling scheme for computing bubble oscillations

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