The Challenge of Simulating Slow Flows in Stellar Astrophysics

Stars spend most of their lives in rather quiescent phases dominated by slow fluid flow, be it low Mach number convection or wave-like motions. Yet accurately modeling these phases is of great importance for understanding mixing in stars, the resulting impact on nucleosynthesis, and the rich data coming from asteroseismology. This influences the ultimate fate of the star and, in turn, galactic chemical evolution.

It turns out that slow flows pose a tough computational challenge for several reasons. Many of the numerical solvers show excessively dissipative behavior at low Mach numbers, which can completely obfuscate the physical solution. Also the very long time scales involved need special treatment, either at the level of the equations or in the time-stepping scheme. Finally, the different physical effects, such as fluid dynamics, gravity, magnetic fields, and nuclear burning, are in a delicate balance, which requires careful coupling.

I will talk about different approaches to solve these challenges and how to make these simulations work efficiently on large supercomputers. In particular I will talk about the merits of implicit time-stepping, well-balancing of different physics terms, and flux functions for all Mach numbers.