Immersed boundary conditions method for unsteady flow problems described by the Laplace operator

An implicit, spectral algorithm for the analysis of unsteady flow problems governed by the Laplace operator in corrugated geometries is described. The algorithm treats the physical boundary conditions as constraints along lines internal to the solution domain. The method eliminates the need for coordinate generation and can be quickly adapted to changing geometries. Various tests confirm the spectral accuracy in space and the first- and second-order accuracies in time. Copyright (C) 2007 John Wiley & Sons, Ltd.