A Framework of Model Reduction with Arbitrary Orders of Accuracy for the Boltzmann Equation

Abstract. 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 [Formula: see text], 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 [Formula: see text], 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 [Formula: see text] in the expansion surprisingly yields models with order of accuracy [Formula: see text]. Furthermore, when the collision term is linearized, the accuracy improves dramatically to [Formula: see text]. 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.