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	Accuracy of the Adaptive GRP Scheme and the Simulation of 2-D Riemann Problems for Compressible Euler Equations
	Han, Ee ; Li, Jiequan ; Tang, Huazhong
	2011
关键词	Adaptive GRP scheme 2-D Riemann problems collapse of a wedge-shaped dam spiral formation shock reflections vortex-shock interaction HYPERBOLIC CONSERVATION-LAWS 2-DIMENSIONAL GAS-DYNAMICS FINITE-ELEMENT-METHOD SINGULAR PROBLEMS TRANSONIC SHOCK FLUID-DYNAMICS HARMONIC MAPS VOLUME METHOD PLANAR SHOCK MESH METHODS
英文摘要	The adaptive generalized Riemann problem (GRP) scheme for 2-D compressible fluid flows has been proposed in [J. Comput. Phys., 229 (2010), 1448-1466] and it displays the capability in overcoming difficulties such as the start-up error for a single shock, and the numerical instability of the almost stationary shock. In this paper, we will provide the accuracy study and particularly show the performance in simulating 2-D complex wave configurations formulated with the 2-D Riemann problems for compressible Euler equations. For this purpose, we will first review the GRP scheme briefly when combined with the adaptive moving mesh technique and consider the accuracy of the adaptive GRP scheme via the comparison with the explicit formulae of analytic solutions of planar rarefaction waves, planar shock waves, the collapse problem of a wedge-shaped dam and the spiral formation problem. Then we simulate the full set of wave configurations in the 2-D four-wave Riemann problems for compressible Euler equations [SIAM J. Math. Anal., 21 (1990), 593-630], including the interactions of strong shocks (shock reflections), vortex-vortex and shock-vortex etc. This study combines the theoretical results with the numerical simulations, and thus demonstrates what Ami Harten observed "for computational scientists there are two kinds of truth: the truth that you prove, and the truth you see when you compute" [J. Sci. Comput., 31 (2007), 185-193].; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000298763800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Physics, Mathematical; SCI(E); 16; ARTICLE; 3; 577-606; 10
语种	英语
出处	SCI
出版者	communications in computational physics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/394367]
专题	数学科学学院
推荐引用方式 GB/T 7714	Han, Ee,Li, Jiequan,Tang, Huazhong. Accuracy of the Adaptive GRP Scheme and the Simulation of 2-D Riemann Problems for Compressible Euler Equations. 2011-01-01.

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