Derivation of L^2-Stable Regularized 13-Moment Equations for Rarefied Gases
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The moment method plays a pivotal role in model reduction within gas kinetic theory. This study focuses on the model reduction of the linear Boltzmann equation under conditions of a relatively small Knudsen number. Through a comprehensive analysis of moment magnitudes, we present a novel regularized 13-moment (R13) system that exhibits the same asymptotic accuracy as the third-order Chapman-Enskog expansion. The newly derived R13 equations demonstrate L^2 stability, owing to their symmetric structure. Building upon this stability, we further develop L^2 stable boundary conditions. Numerical tests are conducted to highlight distinctions between different collision models.
