Efficient solvers for the IBC method

•Efficient solution strategy for immersed boundary conditions method.•Fast linear solvers.•Linear solvers with reduced memory use. Immersed boundary conditions (IBC) method provides an opportunity for spectrally accurate and computationally efficient analysis of flows in complex geometries. The method is limited to domains that are periodic in one direction with top and bottom walls whose heights can be accurately described using Fourier expansions. It is shown that efficiency of this method can be significantly enhanced by the use of a specialized direct linear solver. This solver takes advantage of the particular structure of the coefficient matrix resulting in a significant reduction of both the processing time as well as the memory requirements. Various tests demonstrate a significantly reduced processing time compared to the standard LINPAK/LAPACK solvers. The IBC method combined with the new solver is close to two orders of magnitude faster than algorithms relying on the use of boundary conforming grids. The new solver provides a significant acceleration of time-dependent simulations making the cost of three-dimensional unsteady simulations involving irregular domains comparable to the costs of simulations for regular domains.