Robust layer-resolving methods for various Prandtl problems
Citation:
John Butler, 'Robust layer-resolving methods for various Prandtl problems', [thesis], Trinity College (Dublin, Ireland). School of Mathematics, 2005, pp 232Download Item:
Abstract:
In this thesis we deal with four Prandtl boundary layer problems for
incompressible laminar flow. When the Reynolds and Prandtl numbers are large the
solution of each problem has parabolic boundary layers. For each problem we
construct a direct numerical method for computing approximations to the solution
of the problem using a piecewise uniform fitted mesh technique appropriate to the
parabolic boundary layer. We use the numerical method to approximate the
self-similar solution of the Prandtl problem in a finite rectangle excluding the
leading edge of the wedge, which is the source of an additional singularity caused by
incompatibility of the problem data. We verify that the constructed numerical
method is robust in the sense that the computed errors for the components and
their derivatives in the discrete maximum norm are parameter uniform. For each
problem we construct and apply a special numerical method related to the Blasius
technique to compute a reference solution for the error analysis of the components
and their derivatives. By means of extensive numerical experiments we show that
the constructed direct numerical methods are parameter-uniform.
Author: Butler, John
Advisor:
Miller, J.J HQualification name:
Doctor of Philosophy (Ph.D.)Publisher:
Trinity College (Dublin, Ireland). School of MathematicsNote:
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Mathematics, Ph.D., Ph.D. Trinity College DublinMetadata
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