Arbitrary high order finite volume schemes for linear wave propagation

Abstract

Wave propagation over long distances is usually modeled numerically by high order finite difference schemes, compact schemes or spectral methods. The schemes need good wave propagation properties, i.e. low dispersion and low dissipation. In this paper we show that finite volume schemes may be a good alternative with a number of nice properties. The so called ADER schemes of arbitrary accuracy have been first proposed by Toro et. al. for conservation laws as high order extension of the shock-capturing schemes. In this paper we show theoretically and numerically their dispersion and dissipation properties using the method of differential approximation of Shokin. In two dimensions the stability of these ADER schemes is investigated numerically with the von Neumann method. Numerical results and convergence rates of ADER schemes up to 16th order of accuracy in space and time are shown and compared with respect to the computational effort.