We develop a moment method based on the Hermite series of 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 formulae for low-order situations are simpler and more accurate than some existing results in references. Therefore, one may apply these formulae in slip and jump conditions to improve the accuracy of macroscopic fluid dynamic models for gas flows.

翻译：我们基于任意阶厄米特级数发展了一种矩方法，用于计算一般气体-表面散射核的粘性滑移、热滑移和温度跳跃系数。在散射核的若干常见假设下，通过证明边界条件中对称系数矩阵的正定性获得了可解性。对于采用Cercignani-Lampis气固相互作用和逆幂律分子间势能的气体流动，该模型能以简洁的解析表达式精确捕捉滑移和跳跃系数。一方面，所提出的方法可应用于任意阶矩情形，且精度随阶数提高；另一方面，低阶情形的显式公式比参考文献中的现有结果更简洁精确。因此，可将这些公式应用于滑移和跳跃条件，以提高气体流动宏观流体动力学模型的精度。