动态混合网格生成及隐式非定常计算方法

HYBRID MOVINQ GRID GENERATION AND IMPLICIT ALGORITHM FOR UNSTEADY FLOWS

建立了一种基于动态混合网格的非定常数值计算方法.混合网格由贴体的四边形网格、外场的多层次矩形网格和中间的三角形网格构成.当物体运动时,贴体四边形网格随物体运动而运动,而外场的矩形网格保持静止,中间的三角形网格随之变形;当物体运动位移较大,导致三角形网格的质量降低,甚至导致网格相交时,在局部重新生成网格.新网格上的物理量由旧网格上的物理量插值而得.为了提高计算效率,采用了双时间步和子迭代相结合的隐式有限体积格式计算非定常Navier-stokes方程.子迭代采用高效的块LU-SGS方法.利用该方法数值模拟了NACA0012振荡翼型的无黏和黏性绕流,得到了与实验和他人计算相当一致的结果.

A block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual time-stepping method is developed for moving body problems on hybrid moving grids. To simulate flows over complex configurations, a hybrid grid method is adopted in this paper. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computational domain. Cartesian cells which overlap the quad grids are removed from the computational domain, and a gap is produced between the quad grids and the adaptive Cartesian grid. Finally triangular grids are used to fill this gap. With the motion of moving bodies, the quad grids move with the bodies, while the adaptive Cartesian grid remains stationary. Meanwhile, the triangular grids are deformed according to the motion of solid bodies with a 'spring' analogy approach. If the triangular grids become too skewed, or the adaptive Cartesian grid crosses into the quad grids, the triangular grids are regenerated. Then the flow solution is interpolated from the old to the new grid. The fully implicit equation is solved using a dual time-stepping solver. A Godunov-type scheme with Roe's flux splitting is used to compute the inviscid flux. Several sub-iteration schemes are investigated in this study. Both inviscid and viscous unsteady cases over oscillating NACA0012 airfoil are tested to demonstrate the accuracy and efficiency of the method.