Slip and jump coefficients for general gas-surface interactions according to the moment method

We develop a moment method based on the Hermite series of the arbitrary order to calculate viscous-slip, thermal-slip, and temperature-jump coefficients for general gas-surface scattering kernels. Under some usual assumptions of scattering kernels, the solvability is obtained by showing the positive definiteness of the symmetric coefficient matrix in the boundary conditions. For gas flows with the Cercignani-Lampis gas-surface interaction and inverse-power-law intermolecular potentials, the model can capture the slip and jump coefficients accurately with elegant analytic expressions. On the one hand, the proposed method can apply to the cases of arbitrary order moments with increasing accuracy. On the other hand, the explicit formulas for low-order situations are simpler and more accurate than some existing results in references. Therefore, one may apply these formulas in slip and jump conditions to improve the accuracy of macroscopic fluid dynamic models for gas flows.