Finite Element Formulations for Hyperbolic Systems with Particular Emphasis on the Compressible Euler Equations

Author: Tezduyar, Tayfun Ersin

Year: 1982

Degree: Dissertation (Ph.D.)

Advisor: Wu, Theodore Yao-tsu

Committee Members: Sabersky, Rolf H.; Corngold, Noel Robert; Jennings, Paul C.; Hughes, Thomas J. R.; Wu, Theodore Yao-tsu

Option: Mechanical Engineering

DOI: 10.7907/994z-vj07

Abstract

A Petrov-Galerkin finite element formulation for first-order hyperbolic systems is developed generalizing the streamline approach which has been successfully applied previously to convection-diffusion and incompressible Navier-Stokes equations. The formulation is shown to possess desirable stability and accuracy properties.

The algorithm is applied to the Euler equations in conservation-law form and is shown to be effective in all cases studied, including ones with discontinuous solutions. Accurate and crisp representation of shock fronts in transonic problems is achieved.

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