Volume 19, Issue 5
Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm & Siddhartha Mishra

Commun. Comput. Phys., 19 (2016), pp. 1111-1140.

Published online: 2018-04

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  • Abstract

We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. In particular we consider Euler equations governing compressible flows. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a linear reconstruction procedure satisfying a suitable sign property that helps to maintain entropy stability. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.

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@Article{CiCP-19-1111, author = {}, title = {Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1111--1140}, abstract = {

We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. In particular we consider Euler equations governing compressible flows. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a linear reconstruction procedure satisfying a suitable sign property that helps to maintain entropy stability. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.43s}, url = {http://global-sci.org/intro/article_detail/cicp/11123.html} }
TY - JOUR T1 - Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations JO - Communications in Computational Physics VL - 5 SP - 1111 EP - 1140 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.scpde14.43s UR - https://global-sci.org/intro/article_detail/cicp/11123.html KW - AB -

We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. In particular we consider Euler equations governing compressible flows. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a linear reconstruction procedure satisfying a suitable sign property that helps to maintain entropy stability. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm & Siddhartha Mishra. (2020). Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations. Communications in Computational Physics. 19 (5). 1111-1140. doi:10.4208/cicp.scpde14.43s
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