Finite difference method and a spurious reflection of waves in a layer of fluid
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.
degree of deformation of discrete solutions
scientific article; zbMATH DE number 3954503