A truly three-dimensional (3D) gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work. By local reconstruction of continuous Boltzmann equation, the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver. Different from conventional gas-kinetic scheme, in the present work, the distribution function at cell interface is computed in a straightforward way. As an extension of our previous work (Sun et al., Journal of Computational Physics, 300 (2015) 492–519), the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points. As a result, the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly. To validate the proposed flux solver, several incompressible and compressible viscous flows are simulated. Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows.

中文翻译：

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三维气体动力学通量求解器，用于模拟粘性流，具有保守变量和数值通量的显式公式

在这项工作中提出了一种真正的三维（3D）气体动力学通量求解器，用于模拟不可压缩和可压缩的粘性流。通过局部重建连续的Boltzmann方程，可以在求解器中同时评估通过单元界面的不粘和粘滞通量。与常规的气体动力学方案不同，在本工作中，以简单的方式计算细胞界面处的分布函数。作为我们先前工作的扩展（Sun等人，Journal of Computational Physics，300（2015）492–519），非平衡分布函数是通过单元界面与其周围点之间的平衡分布函数之差来计算的。结果是，可以简单地计算出细胞界面的分布函数，并且可以明确给出用于计算保守的流量变量和通量的公式。为了验证提出的通量求解器，模拟了几种不可压缩和可压缩的粘性流。数值结果表明，该方案可以为三维不可压缩和可压缩的粘性流提供准确的数值结果。