In this paper,we introduce an extension of a splitting method for singularly perturbed equations,the socalled RS-IMEX splitting[Kaiser et al.,Journal of Scientific Computing,70(3),1390–1407],to deal with the fully co...In this paper,we introduce an extension of a splitting method for singularly perturbed equations,the socalled RS-IMEX splitting[Kaiser et al.,Journal of Scientific Computing,70(3),1390–1407],to deal with the fully compressible Euler equations.The straightforward application of the splitting yields sub-equations that are,due to the occurrence of complex eigenvalues,not hyperbolic.A modification,slightly changing the 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 Euler equations;numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.展开更多
文摘In this paper,we introduce an extension of a splitting method for singularly perturbed equations,the socalled RS-IMEX splitting[Kaiser et al.,Journal of Scientific Computing,70(3),1390–1407],to deal with the fully compressible Euler equations.The straightforward application of the splitting yields sub-equations that are,due to the occurrence of complex eigenvalues,not hyperbolic.A modification,slightly changing the 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 Euler equations;numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.
