2025/05/16 by Cai, Zhenning, Li, Ruo, Lu, Yixiao +1
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2505.11184
This paper presents a general framework for constructing reduced models that approximate the Boltzmann equation with arbitrary orders of accuracy in terms of the Knudsen number Kn, applicable to general collision models in rarefied gas dynamics. The framework is based on an orthogonal decomposition of the distribution function into components of different orders in Kn, from which the reduced models are systematically derived through asymptotic analysis. Compared to the Chapman-Enskog expansion, our approach yields more tractable model structures. Notably, we establish that a reduced model retaining all terms up to O(Knn) in the expansion surprisingly yields models with order of accuracy O(Knn+1). Furthermore, when the collision term is linearized, the accuracy improves dramatically to O(Kn2n). These results extend to regularized models containing second-order derivatives. As concrete applications, we explicitly derive 13-moment systems of Burnett and super-Burnett orders valid for arbitrary collision models.