Contributed Talk - Splinter Computation

Friday, 25 September 2020, 16:57   (virtual room B)

Low Mach Number Simulations and Their Need for Well-Balancing

J.P. Berberich, L. Horst, P.V.F. Edelmann, R. Andrassy, J. Higl, C. Klingenberg, F.K. Roepke
Wuerzburg University, HITS, LANL, Heidelberg University

Hydrodynamical simulations of interior convection zones in stars can provide us with critical insight into the structure and evolution of stars. Recent developments in asteroseismology even allow us to observe stochastically excited internal waves created by the convection and therefore to further probe the internal structure. The significance of convectively driven waves in observations is still in discussion which is why we need simulations that can predict the excitation spectra and amplitudes of internal waves as accurately as possible. However, the relevant flows are predicted to have Mach numbers ~ 1e-4, which makes them difficult to resolve numerically, especially for those cases where compressible effects need to be taken into account (e.g., p-modes). Our implicit Seven-League-Hydro Code (SLH) therefore uses specialized low Mach number fluxes that have been developed in the engineering community. However, these systems are numerically rather fragile when simulating strong stratifications and including gravitational source terms, as it is typically the case for astrophysical applications. Tiny interpolation errors during the mapping from a one dimensional stellar evolution model to our multi-dimensional hydro code and other numerical errors due to the discretization of the Euler equations can easily introduce spurious flows that are of the same order of magnitude or even larger than the relevant flows. Well-balancing methods can reduce this kind of errors significantly by exactly maintaining the initial hydrostatic background state. SLH has several well-balancing methods implemented. In this talk we will describe the different methods and show how well-balancing improves our simulations, ultimately allowing us to perform fully compressible simulations at Mach numbers corresponding to the interior of stars.