The Runge–Kutta control volume discontinuous finite element method for systems of hyperbolic conservation laws |
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| Authors: | Dawei Chen Xijun Yu Zhangxin Chen |
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| Affiliation: | 1. The Fifth Lab, Institute of Applied Physics and Computational Mathematics, Beijing 100094, People's Republic of China;2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, People's Republic of China;3. Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N. W. Calgary, Alberta, Canada T2N 1N4 |
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| Abstract: | In this paper, a new high‐order and high‐resolution method called the Runge–Kutta control volume discontinuous finite element method (RKCVDFEM) was proposed to solve 1D and 2D systems of hyperbolic conservation laws. Its main advantage lies in the local conservation, and it is simpler than the Runge–Kutta discontinuous Galerkin finite element method (RKDGM). The theoretical analysis showed that the RKCVDFEM has formally an optimal convergence order for 1D systems. Based on logically rectangular grids of irregular quadrilaterals, a scheme for 2D systems was constructed. Some classical problems were simulated and the validity of the method was presented. Copyright © 2010 John Wiley & Sons, Ltd. |
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| Keywords: | hyperbolic conservation laws Euler equations control volume finite element method discontinuous Galerkin finite element method Runge– Kutta technique logically rectangular grids of irregular quadrilaterals |
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