中文摘要：

降低上面的对称的 Gauss-Seidel (LU-SGS ) 因为它在格子拓扑学，低数字复杂性和谦虚记忆上有更少的相关性的优点，含蓄的松驰广泛地被使用了要求。在原来的 LU-SGS 计划，含蓄的系统矩阵基于切开对流流动 Jacobian 根据被构造它的光谱半径。尽管这个处理有减少计算复杂性和帮助保证含蓄的系统矩阵的斜主导的性质的优点，因为如果 contravariant 速度对声音的速度小或靠近，太多近似被这个切开的方法介绍，它能也在含蓄的系统矩阵上引起严肃的失真。克服这个缺点，有为含蓄的系统矩阵的一个混合构造方法的一个改进 LU-SGS 计划在这份报纸被开发。混合方法是那：在有小 contravariant 速度或接近音速的 contravariant 速度的房间脸上，对流流动术语的精确衍生物被用来构造更多的精确含蓄的系统矩阵，当切开方法的原来的 Jacobian 在另外的房间脸上被采用减少计算复杂性并且保证含蓄的系统矩阵的斜主导的性质时。为了调查改进 LU-SGS 计划， 2D 和 3D 的集中表演，在 NACA0012 机翼， RAE2822 机翼和 LANN 翅膀附近的狂暴的流动在混合未组织的网孔上被模仿。数字结果证明改进 LU-SGS 计划是显著地，比原来的 LU-SGS 有效的更多策划。

英文摘要：

The lower-upper symmetric Gauss-Seidel （LU-SGS） implicit relaxation has been widely used because it has the merits of less dependency on grid topology, low numerical complexity and modest memory requirements. In original LU-SGS scheme, the implicit system matrix is constructed based on the splitting of convective flux Jacobian according to its spectral radius. Although this treatment has the merit of reducing computational complexity and helps to ensure the diagonally dominant property of the implicit system matrix, it can also cause serious distortions on the implicit system matrix because too many approximations are introduced by this splitting method if the contravariant velocity is small or close to sonic speed. To overcome this shortcoming, an improved LU-SGS scheme with a hybrid construction method for the implicit system matrix is developed in this paper. The hybrid way is that： on the cell faces having small contravariant velocity or transonic contravariant velocity, the accurate derivative of the convective flux term is used to construct more accurate implicit system matrix, while the original Jacobian splitting method is adopted on the other cell faces to reduce computational complexity and ensure the diagonally dominant property of the implicit system matrix. To investigate the convergence performance of the improved LU-SGS scheme, 2D and 3D turbulent flows around the NACA0012 airfoil, RAE2822 airfoil and LANN wing are simulated on hybrid unstructured meshes. The nu- merical results show that the improved LU-SGS scheme is significantly more efficient than the original LU-SGS scheme.