A newton-krylov solver with a loosely-coupled
turbulence model for aerodynamic flows
University of Toronto, Department of Aerospace Sciences,
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Computational solutions of the Navier-Stokes equations
have proven to be a useful tool in the design of aircraft.
A Newton-Krylov flow solver for unstructured grids is
developed in order to demonstrate that a formulation in which
the mean-flow and turbulence mechanism equations are loosely coupled
can be more economical than a similar fully-coupled formulation.
The Favre-averaged Navier-Stokes equations are derived for steady
two-dimensional flows, and the turbulence mechanism is described.
These equations constitute a model of the physics of aerodynamic
flows. The model is validated against experimental data. The
objective of this thesis is to examine a means to improve the
iterative process by which the solutions are generated. The
Newton-Krylov iteration is selected in order to refine the solution,
and its features examined. The authors of current Newton-Krylov
techniques have fully coupled the turbulence mechanism to
the Navier-Stokes equations. A contrast and comparison study made here
between the fully-coupled formulation and a loosely-coupled
alternative favours the latter. An `equivalent function
evaluation' metric is selected for comparison purposes, and is
assessed by means of diverse computers. Published results which use
the metric are located, and the present loosely-coupled formulation
for unstructured grids is found to be significantly faster in this
metric than similar fully-coupled formulations. The advantages of the
loosely-coupled formulation with respect to the fully-coupled
formulation are stated and future avenues for exploitation of the
proposed technology are examined. Appendices consist of: a formalism
for the Favre average and consequences of its derivation; a short
tract on Taylor series; and an essay on the Fr\'echet differential.
||Aerodynamics & Flight Mechanics, Fluid Structure Interactions Group
||04 Aug 2008
||16 Apr 2017 17:46
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