A comparison of three velocity discretizations for the Vlasov equation

Conference · Sun Dec 31 04:00:00 EST 1995

OSTI ID:153822

Holloway, J P ^[1]

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1. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering

Three different methods of velocity discretization for the Vlasov equation are compared for use in the numerical solution of the one-dimensional Vlasov equation. The first method is a simple central difference on a uniform grid in velocity space. The other two methods are weighted residuals methods based on Hermite polynomials. Thus all three methods require the same order of computational work, however, for finite numbers of degrees of freedom the finite difference method conserves only particles, the symmetric Hermite method conserves either particles or momentum, while the asymmetric Hermite method conserves particles, momentum, and energy. When used to compute the growth rates of unstable plasma equilibria the finite difference method shows only algebraic convergence, while both Hermite based methods show spectral convergence, with the error decay rate for the asymmetric Hermite method larger than for the symmetric Hermite. Since they cost the same as a finite difference method the Hermite based methods clearly offer an attractive method for Vlasov simulation. The asymmetric Hermite method seems the better: it is more conservative and more accurate for the problems so far examined. One problem with the Hermite methods is that even through the lower numerically computed Hermite moments may be very accurate the pointwise distribution function may be significantly less accurate.

• OSTI ID: 153822
• Report Number(s): CONF-950612--; ISBN 0-7803-2669-5
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BOLTZMANN-VLASOV EQUATION
CALCULATION METHODS
EQUILIBRIUM PLASMA
INSTABILITY GROWTH RATES
PERFORMANCE
PLASMA INSTABILITY
PLASMA SIMULATION