Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres. Explicit Godunov-type schemes with MUSCL reconstruction

GUSTAVO J. KRAUSE

ASTRONOMY AND ASTROPHYSICS

EDP SCIENCES S A

Año: 2019 vol. 631

0004-6361

Context.Many astrophysical processes involving plasma flows are produced in the context of a gravitationally stratified atmospherein hydrostatic equilibrium, in which strong gradients can exist with gas properties that vary in small regions by several orders ofmagnitude. The standard Godunov-type schemes with polynomial reconstruction used to numerically solve these problems fail topreserve the hydrostatic equilibrium owing to the appearance of spurious fluxes generated by the numerical unbalance betweengravitational forces and pressure gradients.Aims.The aim of this work is to present local hydrostatic reconstruction techniques that can be implemented in existing codes withGodunov-type methods to obtain well-balanced schemes that numerically satisfy the hydrostatic equilibrium for various conditions.Methods.The proposed numerical scheme is based on the Godunov method with second order MUSCL-type reconstruction, as isextensively used in astrophysical applications. The difference between the scheme and the standard formulations is only given bycalculating the pressure and density Riemann states on each intercell face and by computing the gravitational source term on eachcell.Results.The local hydrostatic reconstruction scheme is implemented in the FLASH code to verify the well-balanced property forhydrostatic equilibrium with constant or linearly variable temperature and constant or variable gravity. In addition, the behavior ofthe scheme for hydrostatic equilibrium with arbitrary temperature distributions is also analyzed together with the ability to propagatelow-amplitude waves and to capture shock waves.Conclusions.The scheme is demonstrated to be robust and relatively simple to implement in existing codes. This approach producesgood results in hydrostatic equilibrium preservation, satisfying the well-balanced property for the preset conditions and stronglyreducing the spurious fluxes for extreme configurations.