An Investigation of Different Splitting Techniques for the Isentropic Euler Equations
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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 IMEX Runge-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.
J. Zeifang has been supported by the German Research Foundation (DFG) through the International Research Training Group GRK 2160: Droplet Interaction Technologies. K. Kaiser has been partially supported by the German Research Foundation (DFG) through project No. 361/6-1; his study was supported by the Special Research Fund (BOF) of Hasselt University. F. Massa is supported by the Supporting Talented Researchers (STaRS) program of the University of Bergamo. We acknowledge the support and the computing time provided by the High Performance Computing Center Stuttgart (HLRS) through the hpcdg project.
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