Implicit—Explicit Schemes for BGK Kinetic Equations

Authors:
Sandra Pieraccini;Gabriella Puppo
Affiliations:
Dipartimento di Matematica, Politecnico di Torino, Torino, Italia 10129;Dipartimento di Matematica, Politecnico di Torino, Torino, Italia 10129
Venue:
Journal of Scientific Computing
Year:
2007

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Abstract

In this work a new class of numerical methods for the BGK model of kinetic equations is presented. In principle, schemes of any order of accuracy in both space and time can be constructed with this technique. The methods proposed are based on an explicit---implicit time discretization. In particular the convective terms are treated explicitly, while the source terms are implicit. In this fashion even problems with infinite stiffness can be integrated with relatively large time steps. The conservation properties of the schemes are investigated. Numerical results are shown for schemes of order 1, 2 and 5 in space, and up to third-order accurate in time.