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A Petrov-Galerkin Finite Element Formulation for Convection Dominated Flows


Brooks, Alexander Nelson (1981) A Petrov-Galerkin Finite Element Formulation for Convection Dominated Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Q164-VZ22.


In this thesis, a new finite element formulation for convection dominated flows is developed. The basis of the formulation is the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes. When implemented as a consistent Petrov-Galerkin weighted residual method, it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods.

The effectiveness of the streamline upwind/Petrov-Galerkin formulation for the linear advection diffusion equation is demonstrated with numerical examples. The formulation is extended to the treatment of the incompressible Navier-Stokes equations. An efficient implicit pressure/explicit velocity transient algorithm is developed which allows for several treatments of the incompressibility constraint and for multiple iterations within a time step. The algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a Reynolds number of 100.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Civil Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Civil Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hughes, Thomas J. R. (advisor)
  • Housner, George W. (co-advisor)
Thesis Committee:
  • Housner, George W. (chair)
  • Hughes, Thomas J. R.
  • Knowles, James K.
  • List, E. John
Defense Date:15 May 1981
Funding AgencyGrant Number
Electric Power Research InstituteUNSPECIFIED
Stanford UniversityUNSPECIFIED
Record Number:CaltechETD:etd-02012005-161447
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:430
Deposited By: Imported from ETD-db
Deposited On:01 Feb 2005
Last Modified:08 May 2020 20:48

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