456 IGPM456.pdf        August 2016
TITLE A high-order method for weakly compressible flows
AUTHORS Klaus Kaiser, Jochen Schütz
ABSTRACT 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 introduced reference solution splitting [1, 2], which makes use of the incompressible solution. We show that the resulting algorithm is asymptotically consistent (with the asymptotic being Mach number to zero) and asymptotic preserving, and we observe that it is asymptotically stable and asymptotically accurate. Furthermore, we give a systematic way of computing an approximate reference solution by considering the discrete limit method as a potential discretization. The final algorithm is shown to work well on a series of weakly-compressible test cases.
KEYWORDS asymptotic preserving, isentropic incompressible Euler, isentropic compressible Euler, RS-IMEX, IMEX Runge-Kutta, discontinuous Galerkin, low Mach
NOTE updated version of February 1, 2017