In the present work, an adaptive finite-volume numerical scheme has 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 explicit marching scheme. An adaptive algorithm has been developed, which refines the grid locally in order to resolve detected flow features. Employment of non-staggered grid facilitates application of adaptive gridding. A combination of quadrilateral, as well as triangular cells provides flexibility in forming the adaptive grids. Applications of the developed adaptive algorithm include both steady and unsteady flows with different Reynolds numbers. Comparisons with analytical, as well as experimental data evaluate accuracy of the method.
Governing equations and the finite-volume discretization are presented. Next, the adaptive hybrid-grid algorithm is described. Finally, steady as well as unsteady flow simulations are presented, and comparisons with analytical and experimental data are performed.
Related Publications: Kallinderis, Y. and Nakajima K., “A Finite-Element Method for the Incompressible Navier-Stokes Equations with Adaptive Hybrid Grids,” AIAA Paper 93-3005, July 1993.