Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 17, Issue 1-4, Pages 231-240Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1023/A:1015160900410
Keywords
ADER; finite-volume; high order accuracy; linear hyperbolic system; aeroacoustics
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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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