Khái niệm cốt lõi
The authors design and analyze an energy stable, structure preserving, well-balanced and asymptotic preserving (AP) finite volume scheme for the barotropic Euler system with gravity in the anelastic limit.
Tóm tắt
The key aspects of the proposed numerical scheme are:
Energy Stability: The introduction of appropriate velocity shifts in the convective fluxes of mass and momenta ensures the dissipation of mechanical energy.
Well-Balancing: The scheme exactly satisfies the discrete counterparts of the hydrostatic steady states of the Euler system. The stability of solutions with respect to the relative energy leads to well-balancing.
Asymptotic Preserving (AP) Property: The scheme's stability and consistency with the anelastic Euler system is rigorously established as the Mach and Froude numbers vanish. The scheme automatically transitions between the compressible, weakly compressible and the anelastic regimes.
Positivity Preserving: The scheme supports the positivity of density and yields consistency with the weak solutions of the Euler system upon mesh refinement.
The semi-implicit in time and finite volume in space fully-discrete scheme is resolved in two steps: by solving a non-linear elliptic problem for the density and a subsequent explicit computation of the velocity. The authors present results from several benchmark case studies to corroborate the proposed claims.