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A New Class of Nonlinear Finite-Volume Methods for Vlasov Simulation

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2 Author(s)
Jeffrey William Banks ; Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, USA ; Jeffrey Alan Furst Hittinger

Methods for the numerical discretization of the Vlasov equation should efficiently use the phase-space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order nonlinear finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth order in space and time in well-resolved regions but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the piecewise parabolic method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

Published in:

IEEE Transactions on Plasma Science  (Volume:38 ,  Issue: 9 )