Date of Award
Doctor of Philosophy (PhD)
Mechanical & Aerospace Engineering
Robert L. Ash
Manuel D. Salas
Arthur C. Taylor, III
The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using MUSCL-type differencing to obtain state variables at cell interface. Variable interpolations were written in the $\kappa$-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator.
Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-stage predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C° continuity of the grid across the block interface.
The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing, and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility.
Elmiligui, Alaa A..
"Explicit Multistage Schemes for the Solution of the Three-Dimensional Compressible Euler/Navier-Stokes Equations"
(1992). Doctor of Philosophy (PhD), dissertation, Mechanical & Aerospace Engineering, Old Dominion University, DOI: 10.25777/3gxf-m051