Abstract. We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that preserves sharp interfaces. Numerical results reported at the end of the paper are very encouraging, showing the interest of the second order accuracy for genuinely non-linear waves.Résumé. Nous construisons un algorithme d'ordre deux et non dissipatif pour la résolution approchée deséquations d'Euler de la dynamique des gaz compressiblesà deux constituants en dimension un. Le modèle que nous considérons est celuià cinqéquations proposé et analysé dans [1]. L'algorithme est basé sur [8] qui proposait une résolution approchéeà l'ordre un et non dissipative au moyen d'un splitting de type Lagrange-projection. Dans le présent article, nous décrivons, dans le même formalisme, un algorithme d'ordre deux en temps et en espace, qui préserve des interfaces "parfaites" entre les constituants. Les résultats numériques rapportésà la fin de l'article sont très encourageants ; ils montrent clairement les avantages d'un schéma d'ordre deux pour les ondes vraiment non linéaires.

In this paper we present recent developments concerning a Cell-Centered Arbitrary Lagrangian Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction for the numerical simulation of multimaterial compressible fluid flows on general unstructured grids in cylindrical geometries. Especially, our attention is focused here on the following points. First, we propose a new formulation of the scheme used during the Lagrangian phase in the particular case of axisymmetric geometries. Then, the MOF method is considered for multi-interface reconstruction in cylindrical geometry. Subsequently, a method devoted to the rezoning of polar meshes is detailed. Finally, a generalization of the hybrid remapping to cylindrical geometries is presented. These explorations are validated by mean of several test cases that clearly illustrate the robustness and accuracy of the * Corresponding author

In this paper, we present an anti-diffusive method dedicated to the simulation of interface flows on Cartesian grids involving an arbitrary number m of compressible components. Our work is two-fold: first, we introduce a m-component flow model that generalizes a classic two material five-equation model. In that way, interfaces are localized thanks to color function discontinuities and a pressure equilibrium closure law is used to complete this new model. The resulting model is demonstrated to be hyperbolic under simple assumptions and consistent. Second, we present a discretization strategy for this model relying on an Lagrange-Remap scheme. Here, the projection step involves an anti-dissipative mechanism allowing to prevent numerical diffusion of the material interfaces. The proposed solver is built ensuring consistency and stability properties but also that the sum of the color functions remains equal to one. The resulting scheme is first order accurate and conservative for the mass, momentum, energy and partial masses. Furthermore, the obtained discretization preserves Riemann invariants like pressure and velocity at the interfaces. Finally, validation computations of this numerical method are performed on several tests in one and two dimensions. The accuracy of the method is also compared to results obtained with the upwind Lagrange-Remap scheme.

Abstract. We propose a method dedicated to the simulation of interface flows involving an arbitrary number m of compressible components. Our task is two-fold: we first introduce a m-component flow model that generalizes the two-material five-equation model of [2,3]. Then, we present a discretization strategy by means of a Lagrange-Remap [8,10] approach following the lines of [5,7,12]. The projection step involves an anti-dissipative mechanism derived from [11,12]. This feature allows to prevent the numerical diffusion of the material interfaces. We present two-dimensional simulation results of threematerial flow.Résumé. Nous proposons une méthode de simulation pour desécoulements comportant un nombre arbitraire m de composants compressibles séparés par des interfaces. Nous procédons en deuxétapes : tout d'abord nous introduisons un modèle d'écoulementà m composants qui généralise le modèleà cinqéquations de [2,3]. Ensuite nous présentons une stratégie de discrétisation de type LagrangeProjection [8,10] inspirée de [5,7,12]. La phase de projection met en oeuvre une technique de transport anti-diffusive [11,12] qui permet de limiter la diffusion numérique des interfaces matérielles. Nous présentons des résultats de calcul bidimensionnel d'écoulementà trois composants.

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