Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described and selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

Abstract

High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback has been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-by-parts operators and weak boundary conditions during the last 20 years has removed this drawback and now reached a mature state. It is now possible to construct stable and high order accurate multi-block finite difference schemes in a systematic building-block-like manner. In this paper we will review this development, point out the main contributions and speculate about the next lines of research in this area.