The $M_1$ Angular Moments Model in a Velocity-Adaptive Frame for Rarefied Gas Dynamics Applications

Abstract

In the present work the $M_1$ angular moments model in a velocity-adaptive frame is presented for rarefied gas dynamics applications. First of all, the derivation of the angular $M_1$ moments model in the particle mean velocity frame is introduced. The choice of the mean velocity framework in order to enforce the Galilean invariance property of the model is highlighted. In addition, it is shown that the model rewritten in terms of the entropic variables is Friedrichs-symmetric. Also, the derivation of the associated conservation laws and the zero mean velocity condition are detailed. Second, a suitable numerical scheme, preserving the realizable requirement of the numerical solution for the angular $M_1$ moments model in the mean velocity frame, is proposed. Third, some numerical results obtained considering several test cases in different collisional regimes are displayed.