Finite difference method and a spurious reflection of waves in a layer of fluid
type: Item
instance of: scholarly article
title: Finite difference method and a spurious reflection of waves in a layer of fluid
zbMATH Open document ID: 0593.76040
DOI: 10.1016/0045-7825(87)90128-9
author: Kazimierz Szmidt
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: For a layer of fluid and boundary conditions considered in this paper analytical solutions of the Helmholtz equation exist and are well known. When the continuum is replaced by a discrete space of chosen points with a regular grid, analogous solutions may be calculated. In the case of two uniform grids with sudden mesh size change from one grid to the other, in the layer a deformation of discrete solutions occurs. The deformation assumes the form of a spurious wave reflected from the boundary of the two grids. Moreover, the transmitted wave amplitude is changed. If the wave propagates from a grid of smaller mesh size, then the transmitted wave has a larger amplitude than the incident wave. The explicit formulae obtained enable us to calculate the degree of deformation of discrete solutions for the finite difference method and the nonuniform grid.
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3954503
zbMATH Keywords: layer of fluid boundary conditions
zbMATH Keywords: analytical solutions
zbMATH Keywords: regular grid
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: two uniform grids
zbMATH Keywords: sudden mesh size change
zbMATH Keywords: spurious wave
zbMATH Keywords: transmitted wave amplitude
zbMATH Keywords: degree of deformation of discrete solutions
zbMATH Keywords: finite difference method
zbMATH Keywords: nonuniform grid
MaRDI profile type: Publication
full work available at URL: 0045-7825(87)90128-9
OpenAlex ID: W2086005435
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description: scientific article; zbMATH DE number 3954503