Section: New Results
All-speed multi-material schemes
We are interested in the development of numerical models for phenomena involving fluid flows and elastic material deformations. We pursue a monolithic approach, which describes the behavior of each material (gas, liquid or solid) through a system of conservation laws and appropriate constitutive relationships. Our method is designed to handle both high-Mach and low-Mach regimes.
It is well-known that Godunov-type schemes are inadequate for low-Mach problems: first, they introduce an eccessive amount of numerical artificial viscosity; second, they require the enforcement of a CFL stability condition which leads to unpractical time steps. For this reason, we resort to the relaxation method proposed in , to derive a novel discretization scheme which can be applied to problems characterized by a broad range of Mach numbers. As opposed to , we propose in  to treat the advective term implicitly.
Figure 7 shows results for a quasi 1D de Laval nozzle problem in water: the flow is low-Mach and almost incompressible. In the present simulation, we impose at the inlet the total pressure and the absolute temperature and at the outlet the pressure . Figure 7(center) shows results for the explicit scheme proposed in , while Figure 7(right) shows results of our implicit scheme; for the explicit schemes, we impose the acoustic CFL , while for the implicit scheme, we consider . We observe that our method outperforms the method in .