Non-equilibrium Shock Structure Calculation with High-order Modified Navier-Stokes Equations

摘要

High-order modified Navier-Stokes (NS) equations are introduced to describe the transitional flow derived from Burnett equations considering the inaccurate simulation of shock structure using traditional NS continuum methods, particularly at high Mach numbers. This process is performed by defining the effective transportation coefficient, which is associated with Mach number, molecule propriety, and continuum failure criterion. Within this method, the linear Stokes and Fourier relationships are replaced by nonlinear constitutive relationships to describe transitional flow. The traditional NS equation formulation is preserved. The shock structures of both monatomic and diatomic gases are concentrated with different Mach numbers to validate the accuracy and effectiveness of the derived method. The comparison of shock structure with DSMC and Burnett equations shows that the high-order modified NS equations obtain better results than traditional NS equations in terms of shock wave, particularly at high Mach numbers. The modified NS equations also capture the significant features of Burnett equations in shock structure simulation.