高超声速流动计算中LU-SGS隐式算法的应用研究

在高超声速条件下，对原始LU-SGS格式及其改进方法的收敛速度做了深入地比较分析，目的是进一步更好地将LU-SGS算法用于工程上复杂外形的计算模拟当中。二维圆柱，三维钝锥及空天飞机算例的结果表明：(i)对于高超声速粘性流动的计算，粘性项应进行隐式处理；(ii)BLU-SGS方法给出的内迭代方式的收敛性优于DP-LUR方法所给出的内迭代方式；(iii)LU-SGS算法中雅克比系数矩阵的计算方式对计算量及收敛性影响较大，若采用精确的矩阵形式则在流动无分离情况下能取得快速收敛的效果，而在含有流动分离的情况因受稳定性的影响精确的矩阵形式的收敛表现不及对角近似形式。

Study on application of the implicit LU-SGS algorithm for hypersonic flows

Convergence rates of the original LU-SGS scheme and its modified methods have been investigated and compared under hypersonic conditions. The purpose of this paper is to implement the LU-SGS algorithm efficiently for numerical simulation of complex geometries in engineering environment. Numerical results of 2D cylinder, 3D blunt cone and space shuttle show that: (i) the viscous terms must take the implicit form for hypersonic viscous flows; (ii) the convergence rate of the BLU-SGS inner iterations is fast than that in the DP-LUR method; (iii)Jacobian matrices in the LU-SGS algorithm have a significant effect on computational work and convergence performance; for flows without separation, fast convergence can be reached by using the exact matrix method and for flows with large separation, numerical instability makes the exact matrix method inefficient than the diagonal method.