A Taylor Weak Statement Finite Element Algorithm for Real-Gas Compressible Navier-Stokes Simulation

Author

James Downing Freels, University of Tennessee, Knoxville

Date of Award

5-1992

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

Allen J. Baker

Committee Members

Rao V. Arimilli, Eugene L. Wachspress, Jerry E. Stoneking, Osama Soliman

Abstract

A new finite element numerical computational fluid dynamics (CFD) algorithm has been developed for efficiently solving multi-dimensional real-gas compressible flow problems in generalized coordinates on modern parallel-vector computer systems. The algorithm employs a Taylor extension on the classical Galerkin weak statement formulation, a time-relaxed iteration procedure, and a tensor matrix product based factorization of the linear algebra jacobian under a generalized coordinate transformation. Allowing for a general conservation law system, the algorithm has been exercised for the two-dimensional Euler and the laminar and turbulent forms of the Navier-Stokes equations. Equilibrium real-gas air properties are admitted, and numerical results verify solution accuracy, consistency, convergence, efficiency, and stability over a range of test problem parameters. The algorithm is cast in a fully generalized form, such that extension to other flow problems, including three dimensions or two-phase thermal-hydraulics, is direct.

Recommended Citation

Freels, James Downing, "A Taylor Weak Statement Finite Element Algorithm for Real-Gas Compressible Navier-Stokes Simulation. " PhD diss., University of Tennessee, 1992.
https://trace.tennessee.edu/utk_graddiss/4724