Cell-centered Lagrangian scheme for multi-material flows with pressure equilibration

A cell-centered Lagrangian scheme is presented for a multi-material hydrodynamics model with equilibrated material pressures. The scheme is conservative in mass, momentum, and total energy while being entropic per material. This last point is critical for various engineering applications but is seldom addressed. The entropy production in each material is taken as an arbitrary part of the global entropy production hence mimicking different viscosity operators and the underlying vanishing viscosity solution. The scheme is applied to various 1 or 2-dimensional test cases where materials have highly contrasted equations of state. These challenging test cases confirm the robustness of the scheme and show that pressures are kept equal up to the scheme order or even strictly if an additional equilibration procedure is added.