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ADER: A high-order approach for linear hyperbolic systems in 2D. (English) Zbl 1022.76034
Summary: We present the ADER scheme for solving systems of linear, hyperbolic partial differential equations in two dimensions. 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 two-dimensional ADER approach. The linearised Euler equations are used for the simulation of sound emitted by a co-rotating vortex pair.

76M12 Finite volume methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
76B47 Vortex flows for incompressible inviscid fluids
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