粘性流动计算的高品质混合网格生成方法研究

含边界层网格单元的混合网格在粘性流动计算中可取得易用性和计算精度的最佳平衡，针对复杂几何外形和复杂流动，本项目以开发新一代高品质混合网格生成方法为目标，研究解决以下科学难题：1）利用泊松方程建立边界层单元法向推进的全局等价模型，以考虑流场内部含各向异性特征的边界层网格生成问题。相应地，发展泊松方程源项的计算方法和泊松方程的快速多级边界元解法。 2）发展泊松方程的高阶边界元数值解法，以在几何模型的凸边和凸点处集成多法向推进技术，进一步提高复杂几何区域的边界层单元质量。3）建立统一的、同时考虑边界层网格单元和非结构网格单元尺度过渡问题的数学优化模型，开发相应的快速求解算法，实现边界层单元尺寸和非结构单元尺寸的光滑过渡，以提高后续数值计算的精度和效率。上述研究有助于建立成体系的混合网格生成理论及开发新一代高品质混合网格生成软件，并促进其在复杂飞行器粘性流动计算中的应用，有重要的理论和实践意义。

The hybrid mesh with prismatic elements in viscous regions could achieve the best trade-off between ease of use and solution accuracy in the computations of viscous flows. In this proposal, we plan to solve three fundamental issues as below to support the development of the next generation of high-quality hybrid mesh generation method for both complicated geometric models and complicated flows. Firstly, Poisson equations are used as the global control equations for the advancing of marching directions, considering the anisotropic flow features. At the same time, the source function of the equation will be determined and a fast multipole boundary element method will be developed to efficiently solve the equation. Secondly, to incorporate with multiple marching directions, a numerical solution method based on high order boundary elements will be developed to solve the proposed control Poisson equation, aimed at improving the boundary layer mesh quality in complicated geometric regions. Thirdly, to considering the problem of sizing transition of both boundary layer mesh and unstructured mesh, an optimization model will be formulated and solved efficiently, which would provide a smooth transition between the anisotropic sizing of boundary layer mesh and the isotropic sizing of unstructured mesh. It is highly hopeful that the above techniques, once developed successfully as expected, would enable the establishment of the theory of hybrid mesh generation and the development of a new generation of high-quality hybrid mesh generator and their applications in viscous flow simulations for complicated aircraft model.