A finite element method for the incompressible Navier-Stokes equations with adaptive hybrid grids

Abstract

A new adaptive finite-element numerical method hu been developed for the unsteady Navier-Stokes equations of incompressible flow in two dimensions The momentum equations combined with a pressure correction equation are solved employing a non-staggered grid. The solution is advanced in time with an ellplicit/implicit marching scheme. An adaptive algorithm hu been implemented, which refines the grid locally in order to resolve detected flow features. A combination of quadrilateral , u well u triangular cells provides a stable and accu rate numerical treatment of grid interfaces that are located within regions of high gradients. Applications of the developed adaptive algorithm include both steady and unsteady flows, with low and high Reynolds numbers. Comparisons with analytical, u well u experimental data evaluate accuracy and robustness of tile mdhod.