关键词: 计算流体力学, 非结构混合网格, LU-SGS, 线隐式算法, 收敛效率

Abstract:

LU-SGS method is a mainstream time marching algorithm in Computational Fluid Dynamics （CFD）. It reduces computational costs by employing low-order Jacobian matrix approximations such as the maximum spectral radius. However， this approach sacrifices convergence efficiency. Especially in high Reynolds number flow simulations based on unstructured hybrid grid， the numerical stiffness is significantly exacerbated due to the wall-normal direction grid refinement in boundary layer regions， leading to further deterioration in convergence speed and stability. To address these issues， an improved line-implicit BLU-SGS algorithm is proposed. Based on local grid geometric characteristics and flow field physics， this algorithm constructs implicit lines in parallel. By simultaneously solving the coupled equations of control volumes within these implicit lines， the method effectively alleviates the time-step restrictions imposed by small grid scales in the wall-normal direction of boundary layers and enhances the efficiency of upstream-downstream information exchange in far-field regions， thereby achieving a significant acceleration of con-vergence. Additionally， the Jacobian matrix is derived along the implicit lines to ensure consistency with the discretized right-hand side terms of the governing equations. During forward and backward sweeps， the algorithm fully accounts for implicit contributions from off-diagonal blocks to preserve certain nonlinear characteristics of the implicit time marching， further improving convergence efficiency. Numerical validation using benchmark cases such as a 2D flat plate， a 3D M6 wing， and the CHN-T1 aircraft demonstrates that the new algorithm achieves 5-10 times faster convergence compared to the traditional LU-SGS method.

Key words: computational fluid dynamics, unstructured hybrid grids, LU-SGS, line-implicit algorithm, convergence efficiency