An asymptotic-preserving all-speed scheme for fluid dynamics and nonlinear elasticity
An implicit relaxation scheme is derived for the simulation of multidimensional flows at all Mach numbers, ranging from very small to order unity. An analytical proof of the asymptotic-preserving property is proposed and the divergence-free condition on the velocity in the incompressible regime is respected. The scheme possesses a general structure, which is independent of the considered state law and thus can be adopted to solve gas and fluid flows, but also deformations of elastic solids.