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Entropy condition satisfying approximations for the full potential equation of transonic flow

Authors: Stanley Osher, Mohamed Hafez and Woodrow Whitlow
Journal: Math. Comp. 44 (1985), 1-29
MSC: Primary 76H05; Secondary 65M05, 76-08
MathSciNet review: 771027
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Abstract: We shall present a new class of conservative difference approximations for the steady full potential equation. They are, in general, easier to program than the usual density biasing algorithms, and in fact, differ only slightly from them. We prove rigorously that these new schemes satisfy a new discrete "entropy inequality", which rules out expansion shocks, and that they have sharp, steady, discrete shocks. A key tool in our analysis is the construction of an "entropy inequality" for the full potential equation itself. We conclude by presenting results of some numerical experiments using our new schemes.

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Keywords: Full potential equation, transonic flow, entropy condition, difference approximations
Article copyright: © Copyright 1985 American Mathematical Society