High-order well-balanced finite volume schemes for the Euler equations with gravitation
This work provides a simple, easily implementable scheme for astrophysical and other applications requiring accurate preservation of hydrostatic equilibria in Euler equations with gravitation.
The paper presents a high-order well-balanced finite volume scheme for the Euler equations with gravitation that preserves a spatially high-order accurate discrete representation of hydrostatic equilibria, achieving genuine high-order accuracy for smooth solutions near or away from equilibrium. Numerical experiments demonstrate robustness and high-order accuracy.
A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of a large class of hydrostatic equilibria. It is based on a novel local hydrostatic reconstruction, which, in combination with any standard high-order accurate reconstruction procedure, achieves genuine high-order accuracy for smooth solutions close or away from equilibrium. The resulting scheme is very simple and can be implemented into any existing finite volume code with minimal effort. Moreover, the scheme is not tied to any particular form of the equation of state, which is crucial for example in astrophysical applications. Several numerical experiments demonstrate the robustness and high-order accuracy of the scheme nearby and out of hydrostatic equilibrium.