This paper introduces the discrete-velocity-direction model (DVDM) in conjunction with the hyperbolic quadrature method of moments (HyQMOM) to develop a multidimensional spatial-temporal approximation of the BGK equation, termed DVD-HyQMOM. Serving as a multidimensional extension of HyQMOM, DVD-HyQMOM model achieves higher accuracy than other DVDM submodels, especially with an increased number of abscissas. The efficiency and effectiveness of this model are demonstrated through various numerical tests.

翻译：本文引入离散速度方向模型（DVDM）并结合双曲正交矩方法（HyQMOM），构建了BGK方程的多维时空近似模型，称为DVD-HyQMOM。作为HyQMOM的多维扩展，DVD-HyQMOM模型相比其他DVDM子模型具有更高的精度，尤其在增加求积节点数时表现更优。通过多种数值实验验证了该模型的高效性与有效性。