## Mechanical & Aerospace Engineering Theses & Dissertations

Winter 1992

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mechanical & Aerospace Engineering

#### Program/Concentration

Mechanical Engineering

Robert L. Ash

Manuel D. Salas

Osama Kandil

#### Committee Member

Arthur C. Taylor, III

#### Abstract

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.

#### DOI

10.25777/3gxf-m051

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