Application of moment equations to the mathematical simulation of gas microflows

I. E. Ivanov   ; I. A. Kryukov   ; M. Yu. Timokhin

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1721-1738

Résumé

An approach to the simulation of moderately rarefied gas flows in a transition zone is developed. The applicability of the regularized Grad 13-moment (R13) equations to the numerical simulation of a transition flow between the continual and free-molecular gas flow regimes is explored. For the R13 equations, a numerical method is proposed that is a higher order accurate version of Godunov’s explicit method. A numerical procedure for implementing solid-wall boundary conditions is developed. One- and two-dimensional test problems are solved, including the shock wave structure and the Poiseuille flow in a plane channel. The possibility of applying the R13 equations to the simulation of plane channel and jet flows in a transition regime is explored. To this end, the flow in a square cavity generated by the motion of one of the walls is studied and the operation of the Knudsen pump is analyzed.

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