A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes

Abstract

A block lower–upper symmetric Gauss–Seidel (BLU-SGS) implicit dual time-stepping method is developed for moving body problems with hybrid dynamic 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 supersonic and transonic unsteady cases are tested to demonstrate the accuracy and efficiency of the method.