An Investigation of Different Splitting Techniques for the Isentropic Euler Equations

For the accurate and efficient discretization of the low-Mach isentropic Euler equations, which can be used for the description of droplet dynamics, several IMEX splitting schemes have been introduced in literature. In this work, we cast multiple splittings into a common framework, which makes it possible to compare them numerically. Temporal discretization is done with IMEXRunge-Kutta methods, while for the spatial part, we rely on the discontinuous Galerkin spectral element method. It is shown that, while the influence of the splitting on accuracy is small, it has a large impact on efficiency.