Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations. (17th May 2016)

• Record Type: Journal Article
• Authors: Ray, Deep; Chandrashekar, Praveen; Fjordholm, Ulrik S.; Mishra, Siddhartha
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1111
• Page End: 1140
• Publication Date: 2016-05-17
• Subjects: 65M08, -- 35L65, -- 35Q31; Entropy stability, -- Euler equations, -- unstructured grids, -- sign property, -- higher-order accuracy; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.43s
• Languages: English
• ISSNs: 1815-2406

Abstract

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.