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

1977; Elsevier BV; Linguagem: Inglês

10.1016/b978-0-12-460817-7.50009-4

0076-6860

Akio Arakawa, V. R. Lamb,

Advanced Numerical Methods in Computational Mathematics

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.