Research reports

Years: 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

High order discretely well-balanced methods for arbitrary hydrostatic atmospheres

by J. P. Berberich and R. Käppeli and P. Chandrashekar and C. Klingenberg

(Report number 2021-45)

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: finite-volume methods, well-balancing, hyperbolic balance laws, compressible Euler equations with gravity

@Techreport{BKCK21_987,
  author = {J. P. Berberich and R. K\"appeli and P. Chandrashekar and C. Klingenberg},
  title = {High order discretely well-balanced methods for arbitrary hydrostatic atmospheres},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-45},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-45.pdf },
  year = {2021}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).