TY - JOUR
T1 - High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres
AU - P. Berberich , Jonas
AU - Käppeli , Roger
AU - Chandrashekar , Praveen
AU - Klingenberg , Christian
JO - Communications in Computational Physics
VL - 3
SP - 666
EP - 708
PY - 2021
DA - 2021/07
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0153
UR - https://global-sci.org/intro/article_detail/cicp/19307.html
KW - Finite-volume methods, well-balancing, hyperbolic balance laws, compressible Euler equations with gravity.
AB - <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>