UNSTEADY CONFINED VISCOUS FLOWS WITH OSCILLATING WALLS AND MULTIPLE SEPARATION REGIONS OVER A DOWNSTREAM-FACING STEP

This paper presents computational solutions for unsteady viscous flows in channels with a downstream-facing step, followed by an oscillating floor. These solutions of the unsteady Navier–Stokes equations are obtained with a time-integration method using artificial compressibility in a fixed computational domain, which is obtained via a time-dependent coordinate transformation from the fluid domain with moving boundaries. The computational method is first validated for steady viscous flows past a downstream-facing step by comparison with previous numerical solutions and experimental results. This method is then used to obtain solutions for unsteady viscous flows with multiple separation regions over a downstream-facing step with oscillating walls, for which there are no previously known solutions. Thus, the present results may be used as benchmark solutions for the unsteady viscous flows with multiple separation regions between fixed and oscillating walls.