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TVD Finite Element Scheme for Hyperbolic Systems of Conservation Laws

K. Kakuda1, A. Seki1, Y. Yamauchi1
Department of Mathematical Information Engineering, College of Industrial Technology, Nihon University, Chiba 275-8575, Japan.

Computer Modeling in Engineering & Sciences 2010, 69(3), 281-306. https://doi.org/10.3970/cmes.2010.069.281

Abstract

A finite element scheme based on the concept of TVD (total variation diminishing) with a flux-limiter for the hyperbolic systems of conservation laws is presented. The numerical flux is formulated effectively by the weighted integral form using exponential weighting functions. The TVD finite element scheme is applied to a Riemann problem, namely the shock-tube problem, for the Euler system of equations. Numerical results demonstrate the workability and the validity of the present approach through comparison with the exact solutions.

Keywords

Finite element, Petrov-Galerkin method, exponential weighting functions, flux-limiter, TVD.

Cite This Article

Kakuda, K., Seki, A., Yamauchi, Y. (2010). TVD Finite Element Scheme for Hyperbolic Systems of Conservation Laws. CMES-Computer Modeling in Engineering & Sciences, 69(3), 281–306.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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