In this paper, a third-order compact gas-kinetic scheme (GKS) on unstructured tetrahedral mesh is constructed for the compressible Euler and Navier-Stokes solutions. The time-dependent gas distribution function at a cell interface is used to calculate the fluxes for the updating the cell-averaged flow variables and to evaluate the time accurate cell-averaged flow variables as well for evolving the cell-averaged gradients of flow variables. With the accurate evolution model for both flow variables and their slopes, the quality of the scheme depends closely on the accuracy and reliability of the initial reconstruction of flow variables. The reconstruction scheme becomes more challenge on tetrahedral mesh, where the conventional second-order unlimited least-square reconstruction can make the scheme be linearly unstable when using cell-averaged conservative variables alone with von Neumann neighbors. Benefiting from the evolved cell-averaged slopes, on tetrahedral mesh the GKS is linearly stable from a compact third-order smooth reconstruction with a large CFL number. In order to further increase the robustness of the high-order compact GKS for capturing discontinuous solution, a new two-step multi-resolution weighted essentially non-oscillatory (WENO) reconstruction will be proposed. The novelty of the reconstruction includes the following. Firstly, it releases the stability issue from a second-order compact reconstruction through the introduction of a pre-reconstruction step. Secondly, in the third-order non-linear reconstruction, only one more large stencil is added beside those in the second-order one, which significantly simplifies the high-order reconstruction. The proposed third-order scheme shows good robustness in high speed flow computation and favorable mesh adaptability in cases with complex geometry.

翻译：在本文中, 为压缩 Euler 和 Navier- Stokes 解决方案构建了非结构化四面网格的第三级压缩压缩压缩压缩气体动能计划(GKS ) 。 在单元格界面中, 时间依赖气体分配功能用于计算更新单元格平均流变量的通量, 并用于评估时间准确的单元格平均流动变量, 以及用于改变单元格平均流动变量的梯度。 由于流动变量及其斜度的精确进化模型, 计划的质量非常取决于流动变量初始重建的准确性和可靠性。 在四面网路中, 常规的二级无限制最小流动气体分配功能将变得更加棘手。 光是使用单元格平均流动变量更新, 并且用来评估单元格平均流动变量变量变异的斜度。 在四面网路流中, GKS 仅使用四面网路流三级精度的精度平稳重建与大CLFL 的第三级精度重建的精度线性稳定。 为了进一步提高大规模的初始重组的不稳度, 在高端网路路路路路段中, 重建中, 快速重建中, 将显示高端重建中, 快速重建的二线路路路路路路段中, 。