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Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Hyperbolic equations and systems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  17 May 2016

Deep Ray ,
Praveen Chandrashekar ,
Ulrik S. Fjordholm  and
Siddhartha Mishra
Deep Ray*
Affiliation:
Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bengaluru, India
Praveen Chandrashekar*
Affiliation:
Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bengaluru, India
Ulrik S. Fjordholm*
Affiliation:
Department of Mathematical Sciences, NTNU, Trondheim 7491, Norway
Siddhartha Mishra*
Affiliation:
Seminar for Applied Mathematics, ETH Zurich and Center of Mathematics for Applications, University of Oslo, Norway
*
*Corresponding author. Email addresses:deep@tifrbng.res.in (D. Ray), praveen@tifrbng.res.in (P. Chandrashekar), ulrik.fjordholm@math.ntnu.no (U. S. Fjordholm), siddhartha.mishra@sam.math.ethz.ch (S. Mishra)
*Corresponding author. Email addresses:deep@tifrbng.res.in (D. Ray), praveen@tifrbng.res.in (P. Chandrashekar), ulrik.fjordholm@math.ntnu.no (U. S. Fjordholm), siddhartha.mishra@sam.math.ethz.ch (S. Mishra)
*Corresponding author. Email addresses:deep@tifrbng.res.in (D. Ray), praveen@tifrbng.res.in (P. Chandrashekar), ulrik.fjordholm@math.ntnu.no (U. S. Fjordholm), siddhartha.mishra@sam.math.ethz.ch (S. Mishra)
*Corresponding author. Email addresses:deep@tifrbng.res.in (D. Ray), praveen@tifrbng.res.in (P. Chandrashekar), ulrik.fjordholm@math.ntnu.no (U. S. Fjordholm), siddhartha.mishra@sam.math.ethz.ch (S. Mishra)

Abstract

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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.

Keywords

Entropy stabilityEuler equationsunstructured gridssign propertyhigher-order accuracy

MSC classification

Secondary: 65M08: Finite volume methods 35L65: Conservation laws 35Q31: Euler equations

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1111 - 1140
Copyright
Copyright © Global-Science Press 2016 

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