Year: 2021
Author: Jonas P. Berberich, Roger Käppeli, Praveen Chandrashekar, Christian Klingenberg
Communications in Computational Physics, Vol. 30 (2021), Iss. 3 : pp. 666–708
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0153
Communications in Computational Physics, Vol. 30 (2021), Iss. 3 : pp. 666–708
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 43
Keywords: Finite-volume methods well-balancing hyperbolic balance laws compressible Euler equations with gravity.