A Numerical Tool to Compute Hybrid Euler-Lagrange Compressible Models

Abstract

We present in this paper a numerical tool which provides approximations of solutions of hybrid Euler-Lagrange models. The basic underlying ideas of the whole scheme are presented, which rely on the use of relaxation techniques and on a previous investigation of second-moment realisable closures. Numerical tests involving shock and rarefaction waves confirm the suitability of the present approach. The impact of the turbulent noise and the influence of the mesh size are examined.

A Two-Dimensional Relaxation Scheme for the Hybrid Modelling of Two-Phase Flows

“…To overcome this difficulty, a relaxation technique was proposed in [8,9], which is grounded on ideas developed in [3]. It consists in introducing supplementary equations that govern the time evolution of the Reynolds stresses, so that the relaxation system is hyperbolic and preserves the realizability of solutions.…”

A relaxation scheme for hybrid modelling of gas-particle flows

“…Actually, we note that in the conservative system (2), jump relations are defined in a unique way. This essentially differs from the strategy introduced in [25,26,27], where the relaxation system is chosen to be close to the physics and hence contains non-conservative terms active in genuinely non-linear (GNL) fields.…”

“…In the present paper, we are interested in the numerical solution of a system of partial differential equations arising from a hybrid modelling of polydispersed turbulent two-phase flows [10,25,26]. The general framework of the hybrid modelling is recalled in Appendix C, which explains in particular a coupling of Eulerian and Lagrangian descriptions introduced for the modelling of the dispersed phase of gas-particle two-phase flows.…”

“…This approach, which will be referred to as A1, relies on the combined use of relaxation-type techniques [1,4,5,9,12,13,28,35,36,38] and upwinding schemes [14,19,22,23,29,30] and was first introduced in [25] in order to predict single-phase turbulent flows [32]. In the latter approach, an extended hyperbolic system was introduced in a natural way, following what is done for previous associated Eulerian models (see [2,3,6,21]).…”

A simple parameter-free entropy correction for approximate Riemann solvers

“…Sur les maillages les plus grossiers, la perturbation résiduelle au niveau du point sonique est semblableà celle observée pour un schéma de Godunov exact. De nombreuses applicationsà d'autres systèmes deviennent alors envisageables ( [12]). L'extension au cadre multidimensionnel est immédiate.…”