An entropy scheme for the Fokker-Planck collision
operator of plasma kinetic theory |
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| Authors: | Pierre Degond Brigitte Lucquin-Desreux |
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| Institution: | (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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