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Volume 30, Issue 3
High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres

Jonas P. Berberich, Roger Käppeli, Praveen Chandrashekar & Christian Klingenberg

DOI: 10.4208/cicp.OA-2020-0153

Commun. Comput. Phys., 30 (2021), pp. 666-708.

Published online: 2021-07

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  • 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.

  • Keywords

Finite-volume methods, well-balancing, hyperbolic balance laws, compressible Euler equations with gravity.

  • AMS Subject Headings

76M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

klingen@mathematik.uni-wuerzburg.de (Jonas P. Berberich)

  • BibTex
  • RIS
  • TXT
@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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0153}, url = {http://global-sci.org/intro/article_detail/cicp/19307.html} }
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 -

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. Berberich , JonasKäppeli , RogerChandrashekar , Praveen and Klingenberg , Christian. (2021). High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres. Communications in Computational Physics. 30 (3). 666-708. doi:10.4208/cicp.OA-2020-0153
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