Abstract: Numerical investigation was conducted to study the mixing behavior of Stokes flows in a rectangular cavity stirred by alternating motion of three square rods. The square loops of rod moved in two different ways that a Pseudo-Anosov map could be built in the flow domain in the augmented phase space. The finite volume method was used to solve the flow field with the periodic boundary conditions of the rod motion being imposed by the mesh supposition technique. The flow domain was meshed by staggered grids and the discretization schemes for control equations were accurate to the second-order resulting from the use of central differencing. Fluid particle tracking was conducted by a fourth-order Runge-Kutta scheme. The Poincaré section was obtained to reveal the size of the domain in which the Pseudo-Anosov map almost covered the whole cavity region except for four corner zones. The evolution patterns of tracers from different initial positions were computed to characterize the mixing process.Tracer interface stretches experienced exponential increases and had the larger power index than that predicted by the Pseudo-Anosov（pA）map matrix，which was due to the local secondary folding caused by the details of flow field, such as shapes of rods , rod trajectories and so on.

Key words: flow, mixing, numerical simulation, Pseudo-Anosov map, topological chaos, mesh supposition technique

摘要： 对方腔内3个方形搅拌轴两两交替运动引发的Stokes流动的混合问题进行了数值模拟研究。提出了两种搅拌轴方形运动路径来引发相空间内Pseudo-Anosov（pA）映射。采用有限体积方法求解速度场，搅拌轴的周期性速度边界借助叠加网格技术来实现。流动区域采用交错网格划分，控制方程组采用具有二阶精度的中心差分格式离散。粒子运动前锋追踪计算采用具有四阶精度的Runge-Kutta方法实现。得到了Poincaré截面，表明pA起作用的空间尺度几乎覆盖整个方腔，只有4个角区域除外。计算了不同初始位置的示踪剂演化图像来表征混合过程。示踪剂增长将经历指数增长，其增长指数大于pA映射矩阵的预测值，这是由于搅拌轴形状、运动路径等流场细节导致的示踪剂界面局部二次折叠拉伸造成的。

关键词: 流动, 混合, 数值模拟, Pseudo-Anosov映射, 拓扑混沌, 叠加网格技术