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In this series of works, we develop a discrete-velocity-direction model(DVDM) with collisions of BGK-type for simulating gas flows, where themolecular motion is confined to some prescribed directions but the speed isstill a continuous variable in each orientation. In this article, we introducea weighted function in each orientation when recovering the macroscopicparameters. Moreover, the internal molecular degrees of freedom are considered.With this weighted DVDM, we develop three submodels by incorporating thediscrete velocity method, the Gaussian-extended quadrature method of momentsand the Hermite spectral method in each direction. These spatial-time submodelsare novel multidimensional versions corresponding to the three approaches.Numerical tests with a series of 1-D and 2-D flow problems show the efficiencyof the weighted DVDM.

Discrete-velocity-direction models of BGK-type with minimum entropy: II. Weighted models