预估-校正LU-SGS的隐式算法

摘要

In order to improve the efficiency for solving Euler equations, a new prediction - correction LU -SGS scheme is proposed,based on the original LU- SGS scheme.A newly- developed high- efficient Euler equation solver is provided in combination with the high- resolution upwind scheme.The computation efficiency of the prediction - correction LU - SGS scheme, original LU - SGS scheme and GMRES scheme are compared and analyzed respectively, using the transonic inviscid flow surrounding the NACA0012 airfoil and RAE2822 airfoil as two calculation examples.The results shows that the prediction- correction LU-SGS scheme can improve the efficiency remarkably and distinguishably, with its convergence speed enhanced approximately three times than the original LU- SGS scheme and close to the GMRES scheme.%为了进一步提高Euler方程求解效率,在传统LU- SGS格式基础上提出了预估-校正LU- SGS.结合高分辨率迎风通量格式,发展了一套高效的Euler方程求解器.以NACA0012翼型和RAE2822翼型跨音速无粘流动作为算例,对比分析了预估-校正LU- SGS、传统LU- SGS和GMRES格式的计算效率.结果表明:预估-校正LU-SGS算法能显著提高求解效率,其效率接近GMRES算法,比传统LU- SGS方法提高了近三倍.