ИСТИНА

R13 moment set of equations is the regularization of original Grad 13-moment system. Several variants of R13 equations were presented after the first publication. The difference between them lies in the relations for higher order moments. It has been shown that all variants are well applicable for numerical modelling of the moderately rarefied slow gas flows and allow the modelling of main nonequilibrium effects in micro-flow problems. The difficulty is that the solid wall boundary conditions for R13 equations were obtained from one of the variants which is not applicable to near hypersonic flows. This study is devoted to the demonstration of the numerical results of each R13 variant for supersonic flow over the flat plate. The variant of explicit high resolution Godunov scheme with linear flow parameter reconstruction is chosen for numerical solution of the R13 set of equations. Five so-called kinetic boundary conditions are taken as a base of mathematical model of the gas-wall interaction. The complete set of the wall boundary conditions is obtained by an approximation of the selected subset of the R13 bulk equations. The resulted set of nonlinear equations for the wall is solved with Newton’s numerical method. R13 numerical solutions are compared with DSMC results computed by the SMILE++ software system. The analysis of the comparison of R13 numerical results with DSMC data has shown that the best way of correct implementation of this moment system of equations is combine the usage of boundary condition modification near solid wall where gas velocity is small and full nonlinear variant of R13 far from the solid wall.