@Article{CiCP-30-666,
author = {P. Berberich , JonasKäppeli , RogerChandrashekar , Praveen and Klingenberg , Christian},
title = {High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {3},
pages = {666--708},
abstract = {<p style="text-align: justify;">We introduce novel high order well-balanced finite volume methods for the
full compressible Euler system with gravity source term. They require no à 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0153},
url = {http://global-sci.org/intro/article_detail/cicp/19307.html}
}