Towards an h-adaptive immersed boundary method for the unsteady incompressible Navier-Stokes equations

This paper treats the development and validation of a numerical method for the solution of the unsteady incompressible Navier-Stokes equations in two dimensions. The method of choice is a Godunov-type pressure-free correction method similar to the method developed by Lee and LeVeque. Validation is done by considering a two-dimensional boundary-layer flow along a flat-plate. The resulting method provides a starting point for the development of an h-adaptive immersed boundary method to be applied to the flapping flexible filament problem proposed by Zhu and Peskin.