A Spectral Method for Unbounded Domains and Its Application to Wave Equations in Geophysical Fluid Dynamics

摘要

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.