Explicit form of simplified Grad's 13 moments distribution function-based moment gas kinetic solver with unstructured meshes for the multiscale rarefied flow

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.