Date of Award

12-1991

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Aeronautics and Astronautics

First Advisor

Philip Beran, PhD

Abstract

Application of TVD schemes to both inviscid and viscous flows is considered. The mathematical and physical bases of TVD schemes are discussed. First and second-order accurate TVD schemes and a second-order accurate Lax- Wendroff scheme are used to compute solutions to the Riemann problem in order to investigate the capability of each to resolve shocks, rarefactions, and contact surfaces. Second-order finite-volume and finite-difference TVD schemes are used to obtain solutions to inviscid supersonic and transonic cascade flow problems. TVD schemes are shown to be superior to the Lax-Wendroff family of schemes for both transient and steady-state computations. TVD methodology is extended to solution of viscous flow problems. A first-order time accurate, second-order space accurate algorithm is contrasted against a second-order time and space accurate algorithm for solution of the viscous Burgers' equation. Necessity of using the fully second-order accurate algorithm at low Reynolds numbers is shown. Solutions are computed to problems of laminar shock-boundary-layer interaction and unsteady, laminar, shock-induced heat transfer using the new algorithms. These algorithms provide the capability to accurately predict separation, reattachment, and pressure and skin friction profiles for shock- boundary-layer interaction. Extremely accurate comparison with theory and experiment is also evident for the unsteady shock-induced head transfer problem.

AFIT Designator

AFIT-DS-AA-91-2

DTIC Accession Number

ADA243913

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