A large amount of user time and expertise is currently required to obtain accurate computational solutions to compressible flow problems, especially if the geometry or flow field is complex. This presents a barrier for the novice user and an inconvenience for the experienced user. This thesis explores several options for improving this situation.

First, grid-independent solution schemes would relax the current stringent criteria on grid quality. In this context, a grid-independent solution scheme is one which does not require that the grid be aligned with the steepest gradients in the flow. Recent developments in the area of multi-dimensional upwind schemes show promise for reducing grid dependence significantly. In the present work, a multi-dimensional upwind scheme for the Euler equations has been extended in a natural way to solve the Navier-Stokes equations. This approach treats the viscous and inviscid terms together.

Second, automatic grid generation would drastically reduce the amount of work required to obtain a solution — of any quality — for complex geometries. Grid generation for complex, multi-body geometries is presently a formidable task, especially for structured grids. If non-body-fitted Cartesian grids are used, however, grid generation becomes trivial. The prim ary difficulty in using non-body-fitted grids is the enforcement of the solid wall boundary condition. The present work uses Cartesian grids in conjunction with a boundary condition similar to the usual finite volume boundary condition.

Finally, an autom atic grid refinement scheme with the capability to produce and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. recognize a grid-converged solution would obviate the grid-refinement studies currently required to ensure the accuracy of a solution. A refinement scheme has been developed which adds cells based on a measure of the local error in the steady-state solution rather than on derivatives of some flow variable. As such, the scheme can in principle continue to refine until the local error in the solution is everywhere less than some user-specified quantity.

The Navier-Stokes solver and the new Cartesian mesh boundary conditions have been validated. Comparison has been made to several cases for which analytic solutions are known. Inviscid subsonic flow around a biplane configuration was calculated to demonstrate the generality of the grid generation and local refinement schemes. A separated laminar airfoil flow has also been calculated, in conjunction with the autom atic grid refinement scheme. Problems common to Navier-Stokes solvers on Cartesian meshes are discussed.