求解二维Euler方程有限单元边插值的降维重构算法

数值求解二维Euler方程的有限体积法（如k-exact，WENO重构、紧致重构等），无一例外地要进行耗时的网格单元上的二维重构.然而这些二维重构最后仅用于确定网格单元边界上高斯积分点处的解值，单元上二维重构似乎并非必需的.因此，文章提出用网格边上的一维重构来取代有限体积法中网格单元上的二维重构，分别在一致矩形网格和非结构三角形网格上发展了基于网格边重构的求解二维Euler方程的新方法，称为降维重构算法.数值算例表明该算法可以计算有强激波的无黏流动问题，且有较高的计算效率. 

A Lowered Dimension Reconstruction Algorithm Using Finite Element Edge Interpolation for Two-Dimensional Euler Equations

Finite volume methods (such as k-exact, WENO, compact reconstruction, etc) for the two-dimensional Euler equations require time-consuming piecewise two-dimensional (2D) reconstruction unexceptionally. It is found that this 2D reconstruction is used only for evaluating flow variables at Gauss points for calculating numerical fluxes, so the 2D reconstruction seems to be unnecessary. Inspired by this observation, it was proposed to use one-dimensional (1D) reconstruction on the side of a cell to replace the 2D reconstruction on the cell as is the case with finite volume method. For the 2D Euler equations on uniform rectangular grids and unstructured triangular grids a new numerical method (termed as lowered dimension reconstruction algorithm) was developed. Numerical examples show that this algorithm can be used to compute inviscid flow problems with strong shock waves and has good computational efficiency.