Abstract
A spectral method for wave equations on 1D or 2D unbounded domain is proposed. It uses a mapping from a closed domain to an unbounded domain with a standard spectral method for the closed domain. Although the idea to use the mapping is not brand-new, two new ideas are introduced into the spectral method. One is “pseudo-hyper-viscosity”, which prevents spurious wavy errors from growing. The other is a variational formulation of the spectral discretization, which leads to enstrophy conservation so that it can avoid numerical instability. Several application examples for GFD wave equations are shown.Keywordsspectral methodunbounded domainconformai mappinggeophysical fluid dynamicswave equation
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