Simulating flows with moving rigid boundary using immersed-boundary method

The present study is to apply the immersed-boundary method to simulate 2- and 3-D viscous incompressible flows interacting with moving solid boundaries. Previous studies indicated that for stationary-boundary problems, different treatments inside the solid body did not affect the external flow. However, the relationship between internal treatment of the solid body and external flow for moving-boundary problems was not studied extensively and is investigated here. This is achieved via direct-momentum forcing on a Cartesian grid by combining “solid-body forcing” at solid nodes and interpolation on neighboring fluid nodes. The influence of the solid body forcing within the solid nodes is first examined by computing flow induced by an oscillating cylinder in a stationary square domain, where significantly lower amplitude oscillations in computed lift and drag coefficients are obtained compared with those without solid-body-forcing strategy. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L1L1 norm in time and the L2L2 norm in space. Further test problems are simulated to examine the validity of the present technique: 2-D flows over an asymmetrically-placed cylinder in a channel, in-line oscillating cylinder in a fluid at rest, in-line oscillating cylinder in a free stream, two cylinders moving with respect to one another, and 3-D simulation of a sphere settling under gravity in a static fluid. All computed results are in generally good agreement with various experimental measurements and with previous numerical simulations. This indicates the capability of the present simple implementation in solving complex-geometry flow problems and the importance of solid body forcing in computing flows with moving solid objects.