Moment closure approximations of the Boltzmann equation based on \(\varphi \)-divergences. (English) Zbl 1353.35218
The purpose of this paper is to find numerical approximations of Boltzmanns equation by using moments, which is not an easy task considering its high dimensional setting. First the exponential function is approximated by its standard limit definition. Then several approximation methods are outlined: Galerkin approximation, Levermore’s entropy, and Grad’s muliple Hermite polynomial expansion. The divergence-based Tsallis \(q\)-exponential expansion is described, and compared with the Levermore renormalization map. Finally, \(\varphi\)-divergence minimization and symmetric hyperbolicity are considered. Numerical results in one dimension are plotted.
Reviewer: Thomas Ernst (Uppsala)
MSC:
| 35Q20 | Boltzmann equations |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 82C28 | Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics |
| 49M15 | Newton-type methods |
| 65H10 | Numerical computation of solutions to systems of equations |
Keywords:
Boltzmann equation; kinetic theory; moment closure; hyperbolic systems; entropy; divergenceReferences:
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