Volume 27, Issue 3
An Explicit MUSCL Scheme on Staggered Grids with Kinetic-Like Fluxes for the Barotropic and Full Euler System

Thierry Goudon, Julie Llobell & Sebastian Minjeaud

Commun. Comput. Phys., 27 (2020), pp. 672-724.

Published online: 2020-02

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  • Abstract

We present a second order scheme for the barotropic and full Euler equations. The scheme works on staggered grids, with numerical unknowns stored at dual locations, while the numerical fluxes are derived in the spirit of kinetic schemes. We identify stability conditions ensuring the positivity of the discrete density and energy. We illustrate the ability of the scheme to capture the structure of complex flows with 1D and 2D simulations on MAC grids.

  • Keywords

Euler equations, finite volume methods, staggered grids, MUSCL schemes.

  • AMS Subject Headings

65M08, 76M12, 76NXX, 35Q31

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

thierry.goudon@inria.fr (Thierry Goudon)

julie.llobell@laposte.net ( Julie Llobell)

Sebastian.Minjeaud@unice.fr (Sebastian Minjeaud)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-672, author = {Goudon , Thierry and Llobell , Julie and Minjeaud , Sebastian }, title = {An Explicit MUSCL Scheme on Staggered Grids with Kinetic-Like Fluxes for the Barotropic and Full Euler System}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {3}, pages = {672--724}, abstract = {

We present a second order scheme for the barotropic and full Euler equations. The scheme works on staggered grids, with numerical unknowns stored at dual locations, while the numerical fluxes are derived in the spirit of kinetic schemes. We identify stability conditions ensuring the positivity of the discrete density and energy. We illustrate the ability of the scheme to capture the structure of complex flows with 1D and 2D simulations on MAC grids.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0307}, url = {http://global-sci.org/intro/article_detail/cicp/13926.html} }
TY - JOUR T1 - An Explicit MUSCL Scheme on Staggered Grids with Kinetic-Like Fluxes for the Barotropic and Full Euler System AU - Goudon , Thierry AU - Llobell , Julie AU - Minjeaud , Sebastian JO - Communications in Computational Physics VL - 3 SP - 672 EP - 724 PY - 2020 DA - 2020/02 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2018-0307 UR - https://global-sci.org/intro/cicp/13926.html KW - Euler equations, finite volume methods, staggered grids, MUSCL schemes. AB -

We present a second order scheme for the barotropic and full Euler equations. The scheme works on staggered grids, with numerical unknowns stored at dual locations, while the numerical fluxes are derived in the spirit of kinetic schemes. We identify stability conditions ensuring the positivity of the discrete density and energy. We illustrate the ability of the scheme to capture the structure of complex flows with 1D and 2D simulations on MAC grids.

Thierry Goudon, Julie Llobell & Sebastian Minjeaud. (2020). An Explicit MUSCL Scheme on Staggered Grids with Kinetic-Like Fluxes for the Barotropic and Full Euler System. Communications in Computational Physics. 27 (3). 672-724. doi:10.4208/cicp.OA-2018-0307
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