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Computation of nonclassical shocks using a spacetime discontinuous galerkin method

Content Provider	ACM Digital Library
Author	Jegdic, Katarina
Abstract	We present a numerical study for two systems of conservation laws using a spacetime discontinuous Galerkin (SDG) method with causal spacetime triangulations and the piecewise constant Galerkin basis. The SDG method is consistent with the weak formulation of conservation laws, and, in the case of strictly hyperbolic systems, also with the Lax entropy condition. Convergence of the method was shown for a special class of hyperbolic systems (Temple systems).The initial data we consider lead to nonclassical shocks. The first part of our study is for the Keyfitz-Kranzer system. We compute the SDG solutions approximating overcompressive and singular shocks, and note that our results are consistent with those obtained by [Sanders, and Sever 2003] using a finite difference scheme. The second system we consider is an approximation of a three-phase flow in the petroleum reservoirs. Numerical solutions for this system were computed by [Schecter, Plohr, and Marchesin 2004] using the Dafermos regularization and a technique for numerical solving of ordinary differential equations. We compute the SDG approximation to a solution containing a transitional shock.We note that even though convergence of the SDG method was shown so far only for Temple systems, numerical examples herewith show that it can be used successfully in approximating solutions of more general conservation laws.
Starting Page	28
Ending Page	31
Page Count	4
File Format	PDF
ISBN	1595932577
DOI	10.1145/1095242.1095256
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2005-10-19
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Conservation laws Performance of a numerical method Shocks Discontinuous galerkin
Content Type	Text
Resource Type	Article

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