A cartesian/boundary -fitted composite grid method for the Euler and Navier -Stokes equations
A general method based on the composite overlapping grid approach is developed for the solution of the two-dimensional planar or axisymmetric Euler and Favre-averaged Navier-Stokes equations within geometrically complex domains. A fully automated procedure is devised to assemble the component meshes consisting of a single nonuniform Cartesian background mesh and one or more algebraically or hyperbolically generated boundary-fitted meshes. The generalized coordinate form of the flow equations is solved using a robust second-order flux-difference splitting method to spatially discretize the mean flow and Shear Stress Transport turbulence model equations. The tightly coupled system of equations is marched in time using an explicit multistage time stepping scheme. The speed and memory requirements of the scheme are optimized through the use of a structured arrangement for the boundary-fitted grid solution data and an unstructured arrangement for the cartesian grid solution data. Coupling of the solutions within each component grid is achieved by any of three interpolation methods: bilinear (first-order), quadratic (second-order), and a novel viscous adaptation of the second-order multidimensional characteristic boundary point treatment developed here. The viability of the composite grid approach is demonstrated on a variety of inviscid, laminar viscous, and turbulent viscous flowfields through comparisons with exact solutions or experimental data, as well as results using a similar single grid algorithm. Although globally second-order solutions are obtained using any of the interface treatments, minimum solution errors are generally realized using the characteristic scheme. Full overlap of the meshes is shown to be a requirement for adequate solution quality with bilinear interpolation, and for stable solutions using high-order interpolation in the presence of flowfield discontinuities. ^
Major Professor: Joe D. Hoffman, Purdue University.