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Runge-Kutta Upwind Multigrid Multi-Block Three-Dimensional Thin Layer Navier-Stokes Solver, Frank E. Cannizzaro

Mechanical & Aerospace Engineering Theses & Dissertations

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, Upwind numerical techniques, Multigrid acceleration, and Multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available, van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multigrid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with …

Explicit Multistage Schemes For The Solution Of The Three-Dimensional Compressible Euler/Navier-Stokes Equations, Alaa Ahmed Elmiligui

Mechanical & Aerospace Engineering Theses & Dissertations

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, …