For this project, two different numerical schemes are developed for the unsteady Navier-Stokes equations of incompressible flow in two-dimensional space. Emphasis is placed on development of a solver that is stable for high Reynolds numbers. The momentum equations combined with a pressure correction Poisson equation are solved employing a non-staggered grid. The solution is advanced in time with an explicit/implicit two-step marching scheme. Fourth-order artificial dissipation has been used for both momentum and Poisson equations in order to suppress the instability in the velocity and pressure fields. The first scheme is finite-volume, while the second employs finite-element type of discretization. Accuracy, robustness and efficiency of the finite-volume and the finite-element methods are also compared.
An adaptive algorithm is implemented, 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 flow. Comparisons with analytical, as well as experimental data evaluate accuracy of the methods.