Dispersion-relation-preserving finite differene schemes for computational acoustics
type: Item
instance of: scholarly article
title: Dispersion-relation-preserving finite differene schemes for computational acoustics
zbMATH Open document ID: 0790.76057
author: Christopher K. W. Tam
author: Jay C. Webb
published in: Journal of Computational Physics
publication date: 1993-10-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 428551
zbMATH Keywords: free parameter
zbMATH Keywords: seven-point symmetric differencing
zbMATH Keywords: four-level time- stepping
zbMATH Keywords: Laplace transform
zbMATH Keywords: stability
zbMATH Keywords: radiation and outflow boundary conditions
reviewed by: A. I. Tolstykh
MaRDI profile type: Publication
full work available at URL: jcph.1993.1142
OpenAlex ID: W2021121593
DOI: 10.1006/JCPH.1993.1142
description: scientific article; zbMATH DE number 428551