Title page for ETD etd-110498-102120

Type of Document Dissertation
Author Bonhaus, Daryl Lawrence
Author's Email Address d.l.bonhaus@larc.nasa.gov
URN etd-110498-102120
Title A Higher Order Accurate Finite Element Method for Viscous Compressible Flows
Degree PhD
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Grossman, Bernard M. Committee Chair
Anderson, W. Kyle Committee Member
Mason, William H. Committee Member
Schetz, Joseph A. Committee Member
Walters, Robert W. Committee Member
  • Petrov-Galerkin
Date of Defense 1998-11-16
Availability unrestricted
The Streamline Upwind/Petrov-Galerkin (SU/PG) method is applied to higher-order

finite-element discretizations of the Euler equations in one dimension and the Navier-Stokes

equations in two dimensions. The unknown flow quantities are discretized on

meshes of triangular elements using triangular Bezier patches. The nonlinear residual

equations are solved using an approximate Newton method with a pseudotime term. The

resulting linear system is solved using the Generalized Minimum Residual algorithm with

block diagonal preconditioning.

The exact solutions of Ringleb flow and Couette flow are used to quantitatively

establish the spatial convergence rate of each discretization. Examples of inviscid flows

including subsonic flow past a parabolic bump on a wall and subsonic and transonic flows

past a NACA 0012 airfoil and laminar flows including flow past a a flat plate and flow past

a NACA 0012 airfoil are included to qualitatively evaluate the accuracy of the discretiza-tions.

The scheme achieves higher order accuracy without modification. Based on the test

cases presented, significant improvement of the solution can be expected using the higher-order

schemes with little or no increase in computational requirements. The nonlinear sys-tem

also converges at a higher rate as the order of accuracy is increased for the same num-ber

of degrees of freedom; however, the linear system becomes more difficult to solve.

Several avenues of future research based on the results of the study are identified, includ-ing

improvement of the SU/PG formulation, development of more general grid generation

strategies for higher order elements, the addition of a turbulence model to extend the

method to high Reynolds number flows, and extension of the method to three-dimensional

flows. An appendix is included in which the method is applied to inviscid flows in three

dimensions. The three-dimensional results are preliminary but consistent with the findings

based on the two-dimensional scheme.

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