Type of Document Dissertation Author Bonhaus, Daryl Lawrence Author's Email Address email@example.com 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 Keywords
Date of Defense 1998-11-16 Availability unrestricted AbstractThe 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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