4 research outputs found
Well-balanced finite volume schemes for nearly steady adiabatic flows
We present well-balanced finite volume schemes designed to approximate the
Euler equations with gravitation. They are based on a novel local steady state
reconstruction. The schemes preserve a discrete equivalent of steady adiabatic
flow, which includes non-hydrostatic equilibria. The proposed method works in
Cartesian, cylindrical and spherical coordinates. The scheme is not tied to any
specific numerical flux and can be combined with any consistent numerical flux
for the Euler equations, which provides great flexibility and simplifies the
integration into any standard finite volume algorithm. Furthermore, the schemes
can cope with general convex equations of state, which is particularly
important in astrophysical applications. Both first- and second-order accurate
versions of the schemes and their extension to several space dimensions are
presented. The superior performance of the well-balanced schemes compared to
standard schemes is demonstrated in a variety of numerical experiments. The
chosen numerical experiments include simple one-dimensional problems in both
Cartesian and spherical geometry, as well as two-dimensional simulations of
stellar accretion in cylindrical geometry with a complex multi-physics equation
of state