A Local Minimum Aliasing Method for Use in Nonlinear Numerical Models

Abstract

The local spectral method is a minimum aliasing technique for the discretization and numerical integration of prognostic systems consisting of nonlinear partial differential equations. The technique embodies many features of both spectral transform methods and conventional finite difference techniques. The method is derived by applying a digital filtering approximation to a formulation of the nonlinear problem similar to the formulation that leads to the spectral transform method, and shares many of the desirable performance characteristics of that method. In contrast to the spectral transform method, the local spectral method can be implemented on a parallel processing computer system without requiring each processor to have a global knowledge of the values of variables in order to compute spatial derivatives. In addition to the computational virtues of the scheme, the local spectral method should have considerable promise as a high performance scheme for limited area models as appropriate boundary conditions are developed.