Two-fluid compressible simulations on GPU cluster

Abstract

Abstract. In this work we propose an efficient finite volume approximation of two-fluid flows. Our scheme is based on three ingredients. We first construct a conservative scheme that removes the pressure oscillations phenomenon at the interface. The construction relies on a random sampling at the interface [5,6]. Secondly, we replace the exact Riemann solver by a faster relaxation Riemann solver with good stability properties [4]. Finally, we apply Strang directional splitting and optimized memory transpositions in order to achieve high performance on Graphics Processing Unit (GPU) or GPU cluster computations. Résumé. Nous proposons une méthode de volumes finis efficace pour l'approximation d'écoulementsbifluides. Le schémas est basé sur trois ingrédients. Nous construisons d'abord un schéma conservatif sans oscillations de pression. La construction repose sur un échantillonnage aléatoire à l'interface. Ensuite, nous remplaçons le solveur de Riemann exact par un solveur approché de relaxation plus rapide, et qui possède de bonnes propriétés de stabilité. Finalement, nous appliquons un splitting directionnel de Strang et des techniques de transposition optimisées en mémoire pour atteindre de bonnes performances sur GPU ou cluster de GPU.

Modeling binary alloy solidification by a random projection method

“…We now turn to the approximation of the reformulated model (10)-(11)- (7). We adapt the Lagrange-projection method with random sampling remap developed in [38] for the computation of nonclassical shocks of scalar conservation laws, in [33,34] for traffic flow model, in [35] for the interaction of a solid particule with a compressible fluid and in [36,37] for the interface tracking in a compressible two-phase flow. The method consists in two steps.…”

“…In Section 3.2 we provide the algorithm of the random projection step. The projection is active at the moving front only which implies that the scheme is statistically conservative (we refer to [36] for numerical illustrations and [37] for a detailed proof).…”

“…Far from the moving front, a classical monotone numerical flux g T,0 is used. At the interface one uses the numerical fluxes g − T,v and g + T,v (see (37)) that take into account the singular source term in Equation (10) of the temperature T and the concentration c at time t n = nΔt within the cell C i . Let s n be the position of the moving front at time t n , and assume that it coincides with the grid interface s n = x 1/2 .…”

“…Finally Colella had improved the method of Chorin in [30,31], especially by introducing the so-called van der Corput pseudo-random sequence. The technique has been widely used for hyperbolic problems which exhibit sharp discontinuities: in [32] for nonconservative hyperbolic problems for compressible materials, in [33,34] for traffic flow models, in [35] for compressible fluid-particule interaction or in [36,37] for the simulation of two-fluid flows.…”

“…In order to come back to the original mesh, we make use of a random sampling for projecting the moving front at an interface of the original mesh. This technique avoids dealing with moving mesh and, since it is similar to Glimm scheme method [28], it possesses statistically conservation properties (see [37]).…”