Dispersion-relation-preserving finite differene schemes for computational acoustics
The paper deals with constructing high-order difference approximations for the acoustic equations which preserve dispersion relation in the physically relevant range of wave numbers supported by grids. To do this, a free parameter in the seven-point symmetric differencing formula is used to minimize the integrated phase error of the spatial discretization. When considering time discretization, four-level time- stepping is proposed which corresponds to the minimized differences between the real and imaginary parts of the exact and approximate angular frequencies obtained by applying the Laplace transform. The stability of the resulting dispersion-relation preserving (DRP) schemes is investigated. To ensure that the external boundaries of computational domains are transparent to the outgoing disturbances, a set of radiation and outflow boundary conditions compatible with the DRP scheme is developed. To test the performance of the scheme, the results of computations are presented.
radiation and outflow boundary conditions
scientific article; zbMATH DE number 428551