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Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. (English) Zbl 0984.76070

Summary: We present numerical models for computing transitional or rarefied gas flows described by Boltzmann-BGK and BGK-ES equations. We first propose a discrete-velocity model based on the entropy minimization principle. This model satisfies the conservation laws and exhibits the entropy dissipation. Further, we investigate the discretization of velocity derivative appearing in the transport operator. Then we propose some models that satisfy these constraints. Owing to these properties, we obtain numerical schemes that are economic, in terms of discretization, and robust. In particular, we develop a linearized implicit scheme for computing stationary solutions of discrete-velocity BGK and BGK-ES models. This scheme is the basis of a code which can compute high-altitude hypersonic flows, in plane and axisymmetric geometries. Our approach is compared to other methods.

MSC:

76M28 Particle methods and lattice-gas methods
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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