欧拉方程的隐式间断有限元算法研究

摘要

The implicit schemes for solving Euler equation are investigated on unstructured grids, including LU-SGS, GMRES and improved LU-SGS schemes. By Roe numerical flux and Van Albada typed limiter, the traditional LU-SGS and GMRES schemes are explored, and the improved LU-SGS scheme is developed by adding the error compensation of high order term. In addition, the transonic inviscid flow around NACA0012 airfoil and RAE2822 airfoil as the examples are calculated. The numerical experiments indicate that the error compensation LU-SGS algorithm has the advantages of low storage requirements and easy programming, and the computational efficiency is close to GMRES algorithm and more than 2.5 times of LU-SGS one.%针对Euler方程，设计了适合间断Galerkin有限元方法的LU-SGS、GMRES以及修正LU-SGS隐式算法。采用Roe通量以及Van Albada限制器技术实现了经典LU-SGS、GMRES算法，引入高阶项误差补偿，发展了修正LU-SGS算法。以NACA0012、RAE2822翼型为例验证分析了算法的可靠性和高效性。结果表明修正LU-SGS算法存储量较少，程序实现方便，而且计算效率是LU-SGS算法的2.5倍以上，接近于循环GMRES算法。