High order discretely well-balanced methods for arbitrary hydrostatic atmospheres
Abstract
We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not restricted to certain classes of hydrostatic solutions. In one spatial dimension we construct a method that exactly balances a high order discretization of any hydrostatic state. The method is extended to two spatial dimensions using a local high order approximation of a hydrostatic state in each cell. The proposed simple, flexible, and robust methods are not restricted to a specific equation of state. Numerical tests verify that the proposed method improves the capability to accurately resolve small perturbations on hydrostatic states.
Keywords
Cite
@article{arxiv.2005.01811,
title = {High order discretely well-balanced methods for arbitrary hydrostatic atmospheres},
author = {Jonas P. Berberich and Roger Käppeli and Praveen Chandrashekar and Christian Klingenberg},
journal= {arXiv preprint arXiv:2005.01811},
year = {2020}
}
Comments
In this version we added a discussion of well-balanced boundary conditions (Section 2.3.3) and a new test case (Section 3.5)