Application of symbolic algebra to the generation of coordinate transformations

Citation:
Flatau, PJ, Pielke RA, Cotton WR.  1988.  Application of symbolic algebra to the generation of coordinate transformations . Environmental Software. 3:158-160.

Abstract:

In this paper we present tools for automatic generation of generalized (variable and terrain-following) coordinate transformations and its use in numerical models of atmospheric flows. Such methodology should be competitive with the more cornraonly employed nested grid schemes. We discuss the symbolic (computer) algebra program for analytical calculation of Christoffel symbols, metric tensor and other geometrical objects describing a transformation. An example, related to the numerical modeling of mesoscale flows, is given. This example shows how coupled terrain-following m~d stretching transformation can be easily created. The possible application of such methodology in numerical modeling of air pollution on cirrus clouds is briefly discussed.

Notes:

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