Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Engineering Science

Major Professor

Allen J. Baker

Committee Members

J. E. Stoneking, R. V. Arimilli, M. O. Soliman, E. Wachspress


The Taylor Weak Statement has been developed as a potential unified approach for approximate computation of fluid flows. It is verified to contain a variety of numerical dissipative methods developed for advection problems by specific identification of its expansion parameters. Generalized Fourier modal analysis has been completed in one space dimension for both semi-and fully-discrete approximations, from which the flux limiter method is herein developed and evaluated for finite element computations. Its application to 1- and 2-dimensional scalar models is investigated for continuous and discontinuous initial value problems, and its use for the Euler equation system of gas dynamics in 1- and 2-dimensional cases is demonstrated.

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