Stabilized discontinuous Galerkin method for hyperbolic equations |
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Authors: | Jorge LD Calle Sônia M Gomes |
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Affiliation: | a Commodity Systems, R. Dr Jesuí no Maciel, 1738, 04615-005 São Paulo SP, Brazil b Universidade Estadual de Campinas, FEC, Caixa Postal 6021, 13084-971 Campinas SP, Brazil c Universidade Estadual de Campinas, IMECC, Caixa Postal 6065, 13085-970 Campinas SP, Brazil |
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Abstract: | In this work a new stabilization technique is proposed and studied for the discontinuous Galerkin method applied to hyperbolic equations. In order to avoid the use of slope limiters, a streamline diffusion-like term is added to control oscillations for arbitrary element orders. Thus, the scheme combines ideas from both the Runge-Kutta discontinuous Galerkin method J. Scient. Comput. 16 (2001) 173] and the streamline diffusion method Comput. Methods Appl. Mech. Engrg. 32 (1982)]. To increase the stability range of the method, the diffusion term is treated implicitly. The result is a scheme with higher order in space with the same stability range as the finite volume method. An optimal relation between the time step and the size of the diffusion coefficient is analyzed for numerical precision. The scheme is implemented using the object oriented programming philosophy based on the environment described in Comput. Methods Appl. Mech. Engrg. 150 (1997)]. Accuracy and shock capturing abilities of the method are analyzed in terms of two bidimensional model problems: the rotating cone and the backward facing step problem for the Euler equations of gas dynamics. |
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Keywords: | 12 20 82 |
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