fastADER: An Arbitrary High Order Scheme for Linear Acoustics

For the solution of aeroacoustical problems, it is necessary to use high order schemes to resolve the wave propagation accurately over long distances. Sixth order Finite-Difference schemes are used commonly in space, although the discretization method for time integration is often a fourth order accurate Runge Kutta type integration and thus the overall scheme remain fourth order. The fastADER approach is not suffering from the order restriction of the Runge-Kutta schemes, the so called Butcher barrier. The schemes have uniform, arbitrary order in space and time. The schemes can be implemented highly efficiently if the following conditions are fulfilled: globally linearized hyperbolic PDE's discretized on Cartesian grids. The CPU time grows quadratically with the order while no extra memory is needed. In the paper a von Neumann stability test, amplitude and phase error diagrams as well as numerical convergence rates are included thus giving a good overview of the method.