基于离散等价方程的非结构网格有限差分法

激波装配法把解析关系式嵌入流场避免了间断引起的理论问题，使全场一致高精度的实现成为可能，有望解决超声速流动转捩研究中的感受性模拟难题。但装配复杂激波结构以后，被分割的流场空间常出现不规则的几何形状，这给常规的基于结构网格的有限差分法应用带来困难。基于离散等价方程理论，提出了一种新的基于非结构网格的有限差分法，在空间二维离散点附近仅用3条网格线就可以构造出一阶迎风格式。数值算例表明收敛过程对网格质量不敏感，解决了激波装配法模拟激波相交出现小夹角后使用结构网格进行计算存在的难题。根据这种方法的特点展望了未来的应用前景。

Finite difference method for unstructured grid based on discrete equivalent equation

The shock-fitting method embeds the analytical relationship into the flow field to avoid the theoretical problems caused by discontinuity, making it possible to achieve consistent high order scheme in the whole flow field. It is expected to solve the susceptibility simulation problem in the research of supersonic flow transition. However, after complex shock wave structures are fitted, the segmented flow field space often has irregular geometric shapes, bringing difficulties to the conventional finite difference method based on structural mesh. In this paper, based on the theory of discrete equivalence equations, a new finite difference method for unstructured mesh is proposed. In the case of two-dimensional space, a first-order upwind scheme can be constructed by only using three mesh lines at discrete points. Numerical examples show that the convergence process is not sensitive to the quality of the mesh. The proposed scheme is used in the shock-fitting simulation to solve the problem that the structural mesh appears after the shock wave intersects with a small angle. Finally, this paper forecasts the application prospects of the proposed scheme according to its characteristics.