针对高阶间断有限元法的高阶弯曲网格生成技术研究

本项目针对高阶间断有限元法的应用提出一种新的二维和三维高阶网格（即弯曲网格）生成方法。首先采用商业软件生成常规网格；其次，根据生成的物面常规网格信息重构高阶物面，保证物面的光滑连续；再次，以生成的高阶物面为边界条件在生成的常规网格上采用高阶连续有限元数值求解弹性力学方程数值求解，得到变形后的高阶网格。最后，采用并行高阶间断有限元法数值求解二维和三维Euler方程和N-S方程验证生成的高阶网格质量。

A new 2d and 3d high-order mesh (or curved mesh) generation method for high-order DGM (Discontinuous Galerkin Methods) is introduced here. First, ragular mesh is generated using some software; Second, the high-order solid surface of the given geometry is contructed, which is required to be continuous and smooth. Third, the final high-order mesh can be obtained by solving the elastic equations using continuous high-order finite element methods, where the generated smooth solid surface is employed as the boundary condition. Finally, the quality of the generated high-order mesh will be tested by the numericl simulation of the Euler and N-S equations with parallel high-order DG methods.