Modification of temperature jump condition for modified Navier-Stokes equations included molecular diffusivity in high-speed rarefied gas flows

The classical Navier-Stokes (NS) model is inappropriate for the high-speed rarefied gas flow simulations due to the linear NS constitutive relations. A modified NS model has been proposed by incorporating the molecular diffusivity terms in the NS constitutive relations and gave good agreement with the experimental data for simulating the one-dimensional shock wave structure. The current work comprehensively investigates enhancing this modified NS model for two-dimensional high-speed rarefied gas flows and determining its proper slip and jump boundary conditions. A new temperature jump condition is also proposed for this modified NS model. This modified NS model and the new temperature jump condition are implemented in OpenFOAM by modifying the solver rhoCentralFoam, which solves the classical NS equations. Two high-speed gas flow cases are selected to validate the modified NS model with the new temperature jump condition as the sharp leading-edge wedge and truncated leading-edge flat plate with argon as the working fluid. Combining the modified NS equations and the new temperature jump with the wall-function type to correct the viscosity in the Knudsen layer predicts the computational results approaching the DSMC data.