FVCF-NIP method for multi-material compressible fluid flows: some improvements in the computation of condensates evolution.

The purpose of this paper is to describe some improvements in the pure eulerian interface capturing method FVCF-NIP by J.-P. Braeunig, B. Desjardins & J.-M. Ghidaglia. In this method, the interface is sharp and piecewise linear. In a cell containing two materials, termed as mixed cell, each one is pure at both sides of the interface and no diffusion is allowed through it. A conservative scheme is written on each material volume using the condensate formalism which allows in particular sliding of materials on each others. However, material volumes in mixed cells can be tiny and therefore the condition on the time step can be too much restrictive. The conservative scheme is then written with a time step only calculated considering pure cells. In mixed cells, a control procedure is built to ensure a stable evolution in small materials volumes without taking into account the time step constraint

FVCF-NIP method for multi-material compressible fluid flows: some improvements in the computation of condensates evolution.

The purpose of this paper is to describe some improvements in the pure eulerian interface capturing method FVCF-NIP by J.-P. Braeunig, B. Desjardins & J.-M. Ghidaglia. In this method, the interface is sharp and piecewise linear. In a cell containing two materials, termed as mixed cell, each one is pure at both sides of the interface and no diffusion is allowed through it. A conservative scheme is written on each material volume using the condensate formalism which allows in particular sliding of materials on each others. However, material volumes in mixed cells can be tiny and therefore the condition on the time step can be too much restrictive. The conservative scheme is then written with a time step only calculated considering pure cells. In mixed cells, a control procedure is built to ensure a stable evolution in small materials volumes without taking into account the time step constraint

A totally Eulerian Finite Volume solver for multi-material fluid flows: Enhanced Natural Interface Positioning (ENIP)

28 pagesThis work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper Braeunig et al (Eur. J. Mech. B/Fluids, 2009). This Cell-centered Finite Volume method is totally Eulerian since the mesh is not moving and a sharp interface, separating two materials, evolves through the grid. A sliding boundary condition is enforced at the interface and mass, momentum and total energy are conserved. Although this former method performs well on 1D test cases, the interface reconstruction suffers of poor accuracy in conserving shapes for instance in linear advection. This situation leads to spurious instabilities of the interface. The method Enhanced-NIP presented in the present paper cures an inconsistency in the former NIP method that improves strikingly the results. It takes advantage of a more consistent description of the interface in the numerical scheme. Results for linear advection and compressible Euler equations for inviscid fluids are presented to assess the benefits of this new method

An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry.

International audienceIn this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable $\theta$), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific upwinding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity $u_{\theta}$

Some numerical aspects of the conservative PSM scheme in a 4D drift-kinetic code.

The purpose of this work is simulation of magnetised plasmas in the ITER project framework. In this context, kinetic Vlasov-Poisson like models are used to simulate core turbulence in the tokamak in a toroidal geometry. This leads to heavy simulations because a 6D dimensional problem has to be solved, even if reduced to a 5D in so called gyrokinetic models. Accurate schemes, parallel algorithms need to be designed to bear these simulations. This paper describes the numerical studies to improve robustness of the conservative PSM scheme in the context of its development in the GYSELA code. In this paper, we only consider the 4D drift-kinetic model which is the backbone of the 5D gyrokinetic models and relevant to build a robust and accurate numerical method

An algorithm to control the pressure evolution for the FVCF-NIP method for compressible multi-material fluid flows

Journal en ligne : http://www.ijfv.fr/JOURNAL/index.php?name=Downloads&req=viewdownload&cid=21International audienceThe purpose of this paper is to describe a new algorithm for the pure Eulerian interface capturing method FVCF-NIP. In this method, the interface is sharp and piecewise linear. In a cell containing two materials, termed as mixed cell, each one is pure at both sides of the interface and no diffusion is allowed through it. A conservative scheme is written on each material volume using the condensate formalism which allows in particular sliding of materials on each others. However, material volumes in mixed cells can be tiny and therefore the condition on the time step can be too much restrictive. The conservative scheme is then written with a time step only calculated considering pure cells. In mixed cells, a control procedure is built to ensure a stable evolution in small materials volumes. This new algorithm enhances the robustness of the method and allows to simulate a wider range of flow regimes

Sur la simulation d'écoulements multi-matériaux par une méthode eulérienne directe avec capture d'interfaces en dimensions 1, 2 et 3

L'introduction et la conclusion sont en français, le corps du texte en anglais.The method described in this report is designed to simulate multi-material fluid flows, by solving compressible Euler equations with sharp interface capturing, in dimension 2 and 3. Materials are supposed to be non-miscible and to follow different equations of state. The main purpose of this work is to design an interface reconstruction method with no diffusion at all between materials of any eulerian quantity. One novelty of our approach is the use of a pure eulerian finite volume scheme in an interface reconstruction method. A new concept is introduced, the ”condensate”, which allows to handle mixed cells containing two or more materials and to calculate the evolution of the interface on the fixed eulerian grid. Moreover, this method allows a free sliding of materials on each others. The accuracy of the method is evaluated on academic 1D benchmarks and its robustness is tested with severe 2D benchmarks.La méthode présentée dans ce mémoire vise à résoudre numériquement les équations d'Euler en 2D/3D modélisant l'écoulement de plusieurs matériaux compressibles, non-miscibles et de nature différentes. Il s'agit en particulier de reconstruire une interface d'épaisseur nulle entre ces matériaux, sans introduire de mélange entre eux. L'originalité de cette méthode purement eulérienne réside dans l'utilisation d'un schéma volumes finis direct. Le concept de ”condensat” est introduit et étudié dans ce mémoire, qui permet de calculer l'évolution de l'interface dans la grille eulérienne fixe. De plus, cette méthode permet un glissement parfait des matériaux les uns par rapport aux autres et une conservation locale des grandeurs eulériennes. La qualité de la méthode est évaluée par des cas-tests académiques ainsi que par des cas-tests éprouvant la robustesse de la méthod

Contributions à l'étude de schémas numériques de type Volumes Finis et de leurs applications pratiques.

Le contexte de ces travaux est la mise au point de schémas numériques pour l'hydrodynamique compressible multi-matériaux et pour les phases dispersées. En particulier, les sujets d'étude proviennent de difficultés étant apparues dans l'utilisation pratique de ces schémas via des codes de calcul industriels du CEA exploitants des supercalculateurs. En effet, ceux-ci visent à simuler des écoulements réels, i.e. des équations d'état raides, des configurations complexes de matériaux et des écoulements compressibles violents, conditions difficiles qui peuvent faire sortir les méthodes numériques du cadre théorique pour lequel elles ont été conçues. Il est particulièrement visé d'obtenir des schémas robustes, mais précis et convergents pour exploiter à bon escient le raffinement des maillages que va permettre la puissance des futurs supercalcultateurs de classe exascale