Combining Hyperbolic Quadrature Method of Moments and Discrete-Velocity-Direction Models for Solving BGK-type Equations

TL;DR

This paper presents DVD-HyQMOM, a multidimensional model combining DVDM and HyQMOM to solve BGK equations with higher accuracy and efficiency, validated through numerical tests.

Contribution

It introduces DVD-HyQMOM, a novel multidimensional extension of HyQMOM that improves accuracy in solving BGK equations using discrete velocity directions.

Findings

Higher accuracy with increased abscissas.

Demonstrated efficiency through numerical tests.

Outperforms other DVDM submodels.

Abstract

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.