Discrete-velocity-direction models of BGK-type with minimum entropy
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We develop a discrete-velocity-direction model (DVDM) with collisions of BGK-type for simulating gas flows, where the molecular motion is confined to some prescribed directions but the speed is still a continuous variable in each orientation. Analogous to the BGK equation, the discrete equilibriums of the model are determined by minimizing a discrete entropy. We show that the discrete equilibriums exist, converge, and can be efficiently obtained by solving a convex optimization problem. The proposed model facilitates a convenient multidimensional extension of quadrature-based methods of moments. The efficiency and effectiveness of this model are demonstrated through various numerical tests.
