Boundary integral/spectral element solution of the Navier-Stokes equations
Occhialini, James Michael
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https://hdl.handle.net/2142/20590
Description
Title
Boundary integral/spectral element solution of the Navier-Stokes equations
Author(s)
Occhialini, James Michael
Issue Date
1992
Doctoral Committee Chair(s)
Higdon, Jonathan J.L.
Department of Study
Chemical and Biomolecular Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
A boundary integral/spectral element technique was developed to solve the unsteady Navier-Stokes equations and the steady convective transport equation. A semi-implicit formulation of the temporal integration rendered a linear spatial problem at sequential time increments. For low to moderate Reynolds number flows, time stepping tests of the complete method provided stable Navier-Stokes simulations for simple model flows in an arbitrary geometry. The patching of the elemental solution fields into a domain-wide complete solution was achieved by a boundary integral approach. The method offered spectral accuracy in space and admitted high-accuracy discretization in time.
Also, a comprehensive numerical study of convective mass transport from rectangular cavities in low Reynolds number flows was conducted. The flow field was calculated by a high order implementation of the boundary integral method, while the steady-state convective diffusion equation was solved using spectral elements. Numerical convergence tests are presented to show the high precision of these algorithms. Physical results in the form of concentration contours and local mass fluxes are presented for cavity aspect ratios from 1:1 to 4:1 and for Peclet numbers from 0 to 100,000.
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