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.

unsteady incompressible Navier-Stokes equations, pressure-correction method, boundary-layer flow"
Multigrid methods; domain decomposition (msc 65M55), Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (msc 65M60), Navier-Stokes equations (msc 76D05)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Naber, J, & Koren, B. (2007). Towards an h-adaptive immersed boundary method for the unsteady incompressible Navier-Stokes equations. Modelling, Analysis and Simulation [MAS]. CWI.