Dealing with more than two materials in the FVCF–ENIP method

This work concerns the simulation of compressible multimaterial fluid flows and follows up the method Finite Volume with Characteristics Flux for two materials described in paper [R. Loubère, J.P. Braeunig, J.-M Ghidaglia, A totally Eulerian finite volume solver for multimaterial fluid flows: enhanced Natural Interface Positioning (ENIP), Eur. J. of Mech. B Fluids, 31 (4) (2012) 1–11, http://doi:10.1016/j.euromechflu.2011.07.005]. The interface reconstruction method was designed to deal with only two materials. In this paper we present the generalisation of the method to more than two materials. The design principles remain the same as for the two material method. Nevertheless some specific treatments have been added, like an automatic order of treatment of materials using material centres of mass in the so-called condensate. Interestingly the method can accept any interface reconstruction method. For simplicity, the crude onion skin approach with unique material normal has been chosen. The entire scheme has been tested on the four material disc embedded into a reversible incompressible velocity field test case for which numerical error can be computed. Then several more demanding hydrodynamics impacts of droplets on thin film have been simulated to show the ability of the method to qualitatively capture three material complex behaviours (sliding, impact).