An entropy scheme for the Fokker-Planck collisionoperator of plasma kinetic theory |
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Authors: | Pierre Degond Brigitte Lucquin-Desreux |
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Affiliation: | (1) Centre de Math'ematiques et Leurs Applications, U.R.A. 1611, Ecole Normale Sup'erieure de Cachan, 61 avenue du Pr'esident Wilson, F-94235 Cachan Cedex, France , FR;(2) Centre de Math'ematiques et Leurs Applications, U.R.A. 1611, Ecole Normale Sup'erieure de Cachan, 61 avenue du Pr'esident Wilson, F-94235 Cachan Cedex, France , FR |
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Abstract: | Summary. We propose a finite difference scheme to approximate the Fokker-Planck collision operator in 3 velocity dimensions. The principal feature of this scheme is to provide a decay of the numerical entropy. As a consequence, it preserves the collisional invariants and its stationary solutions are the discrete Maxwellians. We consider both the whole velocity-space problem and the bounded velocity problem. In the latter case, we provide artificial boundary conditions which preserve the decay of the entropy. Received October 18, 1993 |
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Keywords: | Mathematics Subject Classification (1991): 65M06 82C40 82C80 82D10 |
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