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Fully compressible magnetohydrodynamic (MHD) simulations are a fundamentaltool for investigating the role of dynamo amplification in the generation ofmagnetic fields in deep convective layers of stars. The flows that arise insuch environments are characterized by low (sonic) Mach numbers (M_son < 0.01). In these regimes, conventional MHD codes typically show excessivedissipation and tend to be inefficient as the Courant-Friedrichs-Lewy (CFL)constraint on the time step becomes too strict. In this work we present a newmethod for efficiently simulating MHD flows at low Mach numbers in aspace-dependent gravitational potential while still retaining all effects ofcompressibility. The proposed scheme is implemented in the finite-volumeSeven-League Hydro (SLH) code, and it makes use of a low-Mach version of thefive-wave Harten-Lax-van Leer discontinuities (HLLD) solver to reduce numericaldissipation, an implicit-explicit time discretization technique based on Strangsplitting to overcome the overly strict CFL constraint, and a well-balancingmethod that dramatically reduces the magnitude of spatial discretization errorsin strongly stratified setups. The solenoidal constraint on the magnetic fieldis enforced by using a constrained transport method on a staggered grid. Wecarry out five verification tests, including the simulation of a small-scaledynamo in a star-like environment at M_son ~ 0.001 . We demonstrate that theproposed scheme can be used to accurately simulate compressible MHD flows inregimes of low Mach numbers and strongly stratified setups even with moderatelycoarse grids.

A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors