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Implicit–Explicit Schemes for BGK Kinetic Equations

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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.

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  1. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italia

    Sandra Pieraccini & Gabriella Puppo

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  1. Sandra Pieraccini
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  2. Gabriella Puppo
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Correspondence to Gabriella Puppo.

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Pieraccini, S., Puppo, G. Implicit–Explicit Schemes for BGK Kinetic Equations. J Sci Comput 32, 1–28 (2007). https://doi.org/10.1007/s10915-006-9116-6

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