Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation

The development of a parallel immersed boundary solver for flows with complex geometries is presented. The numerical method for incompressible Navier-Stokes equations is based on the discrete stream-function formulation and unstructured Cartesian grid framework. The code parallelization is achieved by using the domain decomposition (DD) approach and Single Program Multiple Data (SPMD) programming paradigm, with the data communication among processes via the MPI protocol. A 'gathering and scattering' strategy is used to handle the force computing on the immersed boundaries. Three tests, 3D lid-driven cavity flow, sedimentation of spheres in a container and flow through and around a circular array of cylinders are performed to evaluate the parallel efficiency of the code. The speedups obtained in these tests on a workstation cluster are reasonably good for the problem size up to 10 million and the number of processes in the range of 16-2048.