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Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points

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Title
Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points
Author
Binh, Nguyen Thien
Advisor
Jung, Chang-Yeol
Issue Date
2012-08
Publisher
Graduate School of UNIST
Abstract
In this thesis, we aim to study finite volume approximations which approximate the solutions of convection-dominated problems possessing the so-called interior transition layers. The stiffness of such problems is due to a small parameter multiplied to the highest order derivative which introduces various transition layers at the boundaries and at the interior points where certain compatibility conditions do not meet. Here, we are interested in resolving interior transition layers at turning points. Depending on the characteristics, the latters are identified as turning point layers or characteristic interior layers. The proposed semi-analytic method features interior layer correctors which are obtained from singular perturbation analysis near the turning points. We demonstrate this method is efficient, stable and is of 2nd-order convergence in the approximations.
Description
Mechanical Engineering
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MNE_Theses_Master
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