In this work, we propose a new way of splitting the flux function of the isentropic compressible Euler equations at low Mach number into stiff and non-stiff parts. Following the IMEX methodology, the latter ones are treated explicitly, while the first ones are treated implicitly. The splitting is based on the incompressible limit solution, which we call reference solution (RS). An analysis concerning the asymptotic consistency and numerical results demonstrate the advantages of this splitting.

In this publication, we consider IMEX methods applied to singularly perturbed ordinary differential equations. We introduce a new splitting into stiff and non-stiff parts that has a direct extension to systems of conservation laws and investigate its performance analytically and numerically. We show that this splitting can in some cases improve the order of convergence, demonstrating that the phenomenon of order reduction is not only a consequence of the method but also of the splitting.

In this work, we introduce an IMEX discontinuous Galerkin solver for the weakly compressible isentropic Euler equations. The splitting needed for the IMEX temporal integration is based on the recently introducedreference solutionsplitting [32, 52], which makes use of theincompressiblesolution. We show that the overall method isasymptotic preserving. Numerical results show the performance of the algorithm which is stable under a convective CFL condition and does not show any order degradation.

In this work, we consider the efficient approximation of low-Mach flows by a high-order scheme. This scheme is a coupling of a discontinuous Galerkin (DG) discretization in space and an implicit/explicit (IMEX) discretization in time. The splitting into linear implicit and nonlinear explicit parts relies heavily on the incompressible solution. The method has been originally developed for a singularly perturbed ODE and applied to the isentropic Euler equations. Here, we improve, extend and investigate the so called RS-IMEX splitting method. The resulting scheme can cope with a broader range of Mach numbers without running into roundoff errors, it is extended to realistic physical boundary conditions and it is shown to be highly efficient in comparison to more standard solution techniques.