A Novel Full-Euler Low Mach Number IMEX Splitting (Communications in Computational Physics, 2020)
In this paper, we introduce an extension of a splitting method for singularlyperturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of ScientificComputing, 70(3), 1390–1407], to deal with the fully compressible Euler equations. Thestraightforward application of the splitting yields sub-equations that are, due to theoccurrence of complex eigenvalues, not hyperbolic. A modification, slightly changingthe convective flux, is introduced that overcomes this issue. It is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Eulerequations; numerical results using finite volume and discontinuous Galerkin schemesshow the potential of the discretization.
Keywords: Euler equations; low-Mach; IMEX Runge-Kutta; RS-IMEX.