A Study on Flow Through a Periodic Array of Porous Medium Cylinders by Immersed-Boundary Methods

Numerical simulations with an immersed-boundary method are presented for the incompressible flow past a periodic array of porous-medium cylinders. Fluid/porous-medium interactions are greatly influenced by the accuracy on the interface between the surface of the porous cylinder and the flow around it, because of the sudden change in the governing equations for the fluid and for the porous material. In order to retain the smoothness on the interface, momentum fluxes near the interface are discretized using several schemes, including the 2^nd- and 3^rd-order upwind schemes and the 5^th-order Weighted Essentially Non-Oscillatory (WENO) scheme. These schemes are combined with a direct-forcing immersed-boundary method to remove the discontinuity between the fluid and the porous material, and thus accuracy near the interface can be improved. Low and moderate Reynolds number flows, both outside and inside the porous cylinders, are computed simultaneously by solving a combined governing equation set for incompressible flow. The simulation is first validated using flow over an array of impermeable cylinders. The advantage of high-order schemes is then investigated by looking at the flow parameters near the interfaces between the porous cylinders and the outside flow. Species transport in flow with the porous-cylinder-array configuration is also studied.