Development of a navier stokes solver for compressible flows on cartesian grids with aerodynamics applications

Cartesian grids constitute a special branch in unstructured grid technology. They use specially designed algorithms to generate automatic grids for complex geometries and to simulate flows around such geometries regardless of the body shape and number of bodies. In this dissertation, implementations of generated two- and three-dimensional adaptive refinement/coarsening scheme codes are appended to the developed compressible flow solver by using special Cartesian-based algorithms, namely Ray-Casting method, cut-cell adaptation and curvature adaptation around closed bodies. After the first appearance of Cartesian grid methods for inviscid flows, these techniques have been efficaciously utilized and developed to simulate numerous two- and three-dimensional applications on turbulent flows in the last decade. In this study, it is aimed to generate locally refined hierarchical Cartesian grids for two- and three-dimensional irregular geometries to provide solutions, which are easy to realize and accurate in the case of viscous compressible flows around such geometries. Cartesian grids are generated by constructing a quadtree based data structure in two-dimensional flows and an octree based data structure in three-dimensional flows for the purpose of connecting the Cartesian cells to each other. The goals are to enhance automatic grid generation, to increase convergence rate with local time stepping and multi-grid methods, to facilitate solution adaptation with least squares reconstruction scheme on inviscid (ideal) flows, low Reynolds number viscous (laminar) flows and turbulent flows. As a result, a "hands-off", Cartesian grid generator based flow solver is implemented in object-oriented FORTRAN programming language. Euler equations, Navier-Stokes equations and Reynolds Averaged Navier-Stokes Equations with Spalart-Allmaras turbulence closure are solved for the flows around airfoils and wings. The solutions are validated by comparing the results with experimental and numerical data available in literature.