It is essential to efficiently solve multiscale flows covering the continuum regime to the rarefied regime. The explicit form of Grad's 13 moments distribution function-based moment gas kinetic solver (G13-MGKS) has been proposed in our previous work [Comput. Math. Appl., 137 (2023), pp. 112-125], which demonstrates the potential for efficiently simulating continuum flows accurately and presenting reasonable predictions for rarefied flows at moderate Knudsen numbers on structured meshes. To further extend the solver's applicability to unstructured meshes, we propose the simplified version of the Grad's 13 moments distribution function-based moment gas kinetic solver (SG13-MGKS) with an explicit form of the numerical flux in the present paper. The Shakhov collision model has been adopted and validated within the framework of SG13-MGKS to ensure the correct Prandtl number in the simulation. Additionally, a simplified treatment for the numerical fluxes has been adopted to minimize the need for complex calculations of the gradient of integral coefficients. The performance of SG13-MGKS has been evaluated in numerical cases of Couette flow with temperature differences, flow passing through a NACA0012 airfoil, and pressure-driven flow in a variable-diameter circular pipe. Our results demonstrate that SG13-MGKS can achieve reasonably accurate computational results at Knudsen numbers below 0.2. Benefiting from the avoidance of discretization in velocity space, G13-MGKS is able to be two orders of magnitude faster compared to the conventional discrete velocity method. Furthermore, the simplified form of numerical fluxes and the fewer gradients of integration coefficients enable the performance of SG13-MGKS on unstructured grids with a saving of about 4 times the computation time and 3 times the memory cost compared to the previous version of G13-MGKS.

翻译：高效求解涵盖连续流到稀薄流的多尺度流动至关重要。我们前期工作[Comput. Math. Appl., 137 (2023), pp. 112-125]提出了基于Grad 13矩分布函数的矩量气体动理学求解器（G13-MGKS）的显式形式，该求解器在结构化网格上展示了精确模拟连续流及在中等Knudsen数下合理预测稀薄流的潜力。为将该求解器进一步拓展至非结构化网格，本文提出了一种简化版Grad 13矩分布函数矩量气体动理学求解器（SG13-MGKS），其数值通量具有显式形式。为确保模拟中正确的普朗特数，我们在SG13-MGKS框架内采用并验证了Shakhov碰撞模型。此外，采用简化数值通量处理方法以最大限度降低积分系数梯度的复杂计算需求。通过温度差Couette流、NACA0012翼型绕流及变直径圆管压力驱动流等算例验证，SG13-MGKS在Knudsen数低于0.2时能获得合理精度的计算结果。得益于无需速度空间离散，G13-MGKS的计算速度比传统离散速度法快两个数量级。同时，由于数值通量简化形式及更少的积分系数梯度处理，SG13-MGKS在非结构化网格上的计算时间较G13-MGKS先前版本节省约4倍，内存消耗节省约3倍。