A fast, matrix-free implicit method for compressible flows on unstructured grids
A fast, matrix-free implicit method for compressible flows on unstructured grids
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DOI：
10.1006/jcph.1998.6076
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发表时间：
1998-10
期刊：
影响因子：
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通讯作者：
H. Luo;J. Baum;R. Löhner
中科院分区：
文献类型：
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作者：
H. Luo;J. Baum;R. Löhner
一个快速，矩阵自由隐式方法已开发解决三维可压缩欧拉和Navier？非结构网格上的Stokes方程。由牛顿线性化产生的线性方程组的近似系统求解的GMRES（广义最小残差）算法与LU-SGS（低？上对称高斯Seidel）预条件子。GMRES+LU-SGS方法的一个显著特点是通过数值通量逼近雅可比矩阵，完全消除了雅可比矩阵的存储，从而得到一种无矩阵隐式方法。该方法已用于计算从亚音速到超音速的各种流动条件下三维复杂气动外形的可压缩流动。得到的数值结果表明，使用GMRES+LU-SGS方法导致显着增加性能超过目前最好的隐式方法，GMRES+ILU和LU-SGS，同时保持内存要求类似于其显式对应。一个整体的加速因子从八到一个以上的数量级的所有测试用例相比，显式方法证明。
A fast, matrix-free implicit method has been developed to solve the three-dimensional compressible Euler and Navier?Stokes equations on unstructured meshes. An approximate system of linear equations arising from the Newton linearization is solved by the GMRES (generalized minimum residual) algorithm with a LU-SGS (lower?upper symmetric Gauss?Seidel) preconditioner. A remarkable feature of the present GMRES+LU-SGS method is that the storage of the Jacobian matrix can be completely eliminated by approximating the Jacobian with numerical fluxes, resulting in a matrix-free implicit method. The method developed has been used to compute the compressible flows around 3D complex aerodynamic configurations for a wide range of flow conditions, from subsonic to supersonic. The numerical results obtained indicate that the use of the GMRES+LU-SGS method leads to a significant increase in performance over the best current implicit methods, GMRES+ILU and LU-SGS, while maintaining memory requirements similar to its explicit counterpart. An overall speedup factor from eight to more than one order of magnitude for all test cases in comparison with the explicit method is demonstrated.