Introduction to diffuse interfaces and transformation fronts modelling in compressible media

Richard Saurel^1, 2 ; Fabien Petitpas^1, 2

¹ Aix-Marseille Université, CNRS, IUSTI UMR 7343, 5 rue E. Fermi, 13453, Marseille, France
² Also, RS2N, Bastidon de la Caou, 13360 Roquevaire, France

ESAIM. Proceedings, Tome 40 (2013), pp. 124-143.

Résumé

Computation of interfaces separating compressible materials is related to mixture cells appearance. These mixture cells are consequences of fluid motion and artificial smearing of discontinuities. The correct computation of the entire flow field requires perfect fulfillment of the interface conditions. In the simplest situation of contact interfaces with perfect fluids, these conditions correspond to equal normal velocities and equal pressures. To compute compressible flows with interfaces two main classes of approaches are available. In the first one, the interface is considered as a sharp discontinuity. Lagrangian, Front Tracking and Level Set methods belong to this class. The second option consists in the building of a flow model valid everywhere, in pure materials and mixture cells, solved routinely with a unique Eulerian algorithm [37]. In this frame, the interface is considered as a numerically diffused zone, captured by the algorithm. There are some advantages with this approach, as the corresponding flow model is not only valid in artificial mixture cells, but it also describes accurately true multiphase mixtures of materials. The [37] approach has been simplified by [22] with the help of asymptotic analysis, resulting in a single velocity, single pressure but multi-temperature flow model. This reduced model presents however difficulties for its numerical resolution as one of the equations is non-conservative. In the presence of shocks, jump conditions have been provided by [42], determined in the weak shock limit. When compared against experiments for both weak and strong shocks, excellent agreement was observed. These relations have been accepted as closure shock relations for the [22] model and allowed the study of detonation waves in heterogeneous energetic materials. Generalized Chapman-Jouguet conditions were obtained as well as heterogenous explosives (non-ideal) detonation wave structures [36]. Oppositely to the previous example of exothermic reactions and high speed flows, endothermic reactions are considered in [43] to deal with cavitating and flashing flows. In conjunction with capillary [33] and diffusive effects, it has been possible to deal with boiling flows [25]. Extra multiphysic extensions such as dynamic powder compaction [38], solid-fluid coupling in extreme deformations [12] have been investigated too.

Détail

DOI : 10.1051/proc/201340008