Discrete-Velocity-Direction Models of BGK-Type with Minimum Entropy: II—Weighted Models

In this series of works, 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. In this article, we introduce a weighted function in each orientation when recovering the macroscopic parameters. Moreover, the internal molecular degrees of freedom are considered. With this weighted DVDM, we develop three submodels by incorporating the discrete velocity method, the Gaussian-extended quadrature method of moments and the Hermite spectral method in each direction. These spatial-time submodels are novel multidimensional versions corresponding to the three approaches. Numerical tests with a series of 1-D and 2-D flow problems show the efficiency of the weighted DVDM.