| Analysis and experiment in nonlinear computational stability - :12525 | National Weather Service (NWS)
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Analysis and experiment in nonlinear computational stability
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    New extensions of Phillips' (1959) computational stability analysis to several finite-difference forms yield some interesting explanations of what is generally observed when nonlinear computational instability sets in. The one-dimensional shock equation has been adopted for the analyses, and in spite of its apparent simplicity it is capable of describing many features of both stable and unstable calculations with the full set of atmospheric equations. The analyses, among other things, are used to investigate the validity of some ideas which have been proposed in the past as root causes of nonlinear instability. Among the analyses are cases in which cascade of energy is permitted in the spectrum but energy is not trapped in the high wave numbers, unstable cases in which aliasing is not permitted, and cases in which the computational mode can be a stabilizing factor. The so-called "energy-conservation" form is partially analyzed, and shown to have a stability criterion similar to the others.

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