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Finite element methods are a common tool to solve problems in computational fluid dynamics (CFD). This thesis explores the finite element package deal.ii and specific applications to incompressible CFD. Some notation and results from finite element theory are summarised, and a brief overview of some of the features of deal.ii is given. Following this, several CFD applications are presented, including the Stokes equations, the Navier-Stokes equations and the equations for Darcy flow in porous media. Comparison with benchmark problems are provided for the Stokes and Navier-Stokes equations and a case study looking at foam deformation is provided for Darcy flow. Code is provided where applicable.
A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science.
Includes bibliographical references.
Janet Peterson, Professor Co-Directing Thesis; Sachin Shanbhag, Professor Co-Directing Thesis; John Burkardt, Committee Member.
Florida State University
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