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The spacetime conservation element-solution element (CE/SE) method is extended to two-dimensional incompressible viscous flow in a two-sided lid-driven square cavity.Based on the SIMPLE method concept,the preconditioned dual-time scheme is introduced for unsteady computations.The CE/SE-based code is validated by simulating one-sided lid-driven cavity flows.The two-sided lid-driven square cavity problem involves several interesting characteristics being successfully predicted,including development of a pair of off-coer vortices and a free shear layer in the case of parallel wall motion,as well as the appearance of coer vortices for lower Reynolds numbers in the case of anti-parallel motion of the walls.It is found that both the Reynolds number and the direction of the moving walls affect the fluid flow in the cavity.