Moment equations of a conservative multigroup approximation to the nonlinear 3D Boltzmann equation. (English) Zbl 1127.82312
Summary: We propose conservative model Boltzmann equations, which are flexible enough to fit the special requirements of numerical calculations. The connection of a revised multigroup approach (RMA) and a spherical harmonics expansion leads to a set of partial differential equations describing the temporal and spatial evolutions of terms closely related to macroscopic quantities. Moreover, it is proved that this model contains the exact conservation laws for particle density, momentum, and energy density. The applicability of the model is demonstrated in both time dependent and a steady space dependent fluid dynamical situation by comparing the relaxation of a gas with the BKW mode and by considering the Kramer problem.
MSC:
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
Keywords:
Boltzmann equation; conservative model equations; revised multigroup approach; Kramer problemReferences:
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