ADER schemes for three-dimensional non-linear hyperbolic systems

Authors:
V. A. Titarev;E. F. Toro
Affiliations:
Department of Mathematics, Faculty of Science, University of Trento, Trento, Povo 38080, Italy;Laboratory of Applied Mathematics, Faculty of Engineering, University of Trento, Trento, Italy
Venue:
Journal of Computational Physics
Year:
2005

Citing 12
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Abstract

In this paper, we carry out the extension of the ADER approach to multidimensional non-linear systems of conservation laws. We implement non-linear schemes of up to fourth order of accuracy in both time and space. Numerical results for the compressible Euler equations illustrate the very high order of accuracy and non-oscillatory properties of the new schemes. Compared to the state-of-art finite-volume WENO schemes the ADER schemes are faster, more accurate, need less computer memory and have no theoretical accuracy barrier.