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ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D

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Abstract

The ADER scheme for solving systems of linear, hyperbolic partial differential equations in two-dimensions is presented in this paper. It is a finite-volume scheme of high order in space and time. The scheme is explicit, fully discrete and advances the solution in one single step. Several numerical tests have been performed. In the first test case the dissipation and dispersion behaviour of the schemes are studied in one space dimension. Dispersion as well as dissipation effects strongly influence the discrete wave propagation over long distances and are very important for, e.g., aeroacoustical calculations. The next test, the so-called co-rotating vortex pair, is a demonstration of the ideas of the two-dimensional ADER approach. The linearised Euler equations are used for the simulation of the sound emitted by a co-rotating vortex pair.

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Authors and Affiliations

  1. Institute for Aero- and Gasdynamics (IAG), University of Stuttgart, Germany

    T. Schwartzkopff & C. D. Munz

  2. Department of Computing and Mathematics, Manchester Metropolitan University, Manchester, United Kingdom

    E. F. Toro

Authors
  1. T. Schwartzkopff
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  2. C. D. Munz
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  3. E. F. Toro
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Schwartzkopff, T., Munz, C.D. & Toro, E.F. ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D. Journal of Scientific Computing 17, 231–240 (2002). https://doi.org/10.1023/A:1015160900410

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  • DOI: https://doi.org/10.1023/A:1015160900410

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