Finite element formulations for hyperbolic systems with particular emphasis on the compressible Euler equations

Citation

Tezduyar, Tayfun E. (1982) Finite element formulations for hyperbolic systems with particular emphasis on the compressible Euler equations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-09112006-130749

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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