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Near-wall similarity in three-dimensional turbulent boundary layersTennant, Mark Harris 15 July 2010 (has links)
This work investigates three main topics. The first of these is the development and comparison of time integration schemes on two-dimensional unstructured meshes. Both explicit and implicit solution algorithms for the two-dimensional Euler equations on unstructured grids are presented. Cell-centered and cell-vertex finite volume upwind schemes utilizing Roe’s approximate Riemann solver are developed. For the cell-vertex scheme, a four stage Runge-Kutta time integration with and without implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method, and two methods utilizing preconditioned sparse matrix solvers are investigated. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit LU decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver in order to decrease CPU time by reducing the fill of the Jacobian matrix. Comparisons are made for both first-order and higher-order accurate solutions using several different time integration algorithms. Higher-order accuracy is achieved by using multi-dimensional monotone linear reconstruction procedures. Results for flow over a transonic circular arc are compared for the various time integration methods. The second topic involves an interactive adaptive remeshing algorithm. The interactive adaptive remeshing algorithm utilizing a frontal grid generator is compared to a single grid calculation. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. Solutions for two-dimensional, inviscid flow over a transonic circular arc and a Mach 3.0 internal flow with an area change are examined. The final topic examined in this work is the capabilities developed for a structured three-dimensional code called GASP. The capabilities include: generalized chemistry and thermodynamic modeling, space marching, memory management through the use of binary C Input/Ouput, and algebraic and two-equation eddy viscosity turbulence modeling. Results are given for a Mach 1.7 three-dimensional analytic forebody, a Mach 1.38 axisymmetric nozzle with hydrogen-air combustion, a Mach 14.1 15° ramp, and Mach 0.3 viscous flow over a flat plate. The incorporation of these capabilities and the two-dimensional unstructured time integration schemes into a three-dimensional unstructured solver is also discussed. / Ph. D.
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