| Problems of biological fluid mechanics often involve the interaction of a viscous incompressible fluid with an elastic membrane. One can consider this membrane as a boundary immersed in the fluid. The Immersed Boundary Method was designed to solve this kind of problem. The main idea of this method is to use a regular Eulerian computational grid for the fluid mechanics together with a Lagrangian representation of the immersed boundary. The boundary applies a singular force to the fluid and at the same time it moves at the local fluid velocity. One common question about this method is how the numerical scheme performs at different Reynolds numbers. We address this question by simulating the flow past an array of cylinders, a classical fluid dynamics problem. The Immersed Boundary Method calls a Navier-Stokes solver as a subroutine, and we study the effect of this fluid solver on the accuracy of the computation. We find that there is considerable benefit to the use of a second order accurate fluid solver despite the fact that the Immersed Boundary Method, as presently formulated, is only first order accurate. The benefit comes from a reduction in numerical viscosity, as revealed in the calculation of drag. |
