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.

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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.