Applied Mathematics Commons^™

Dynamic Meshing Around Fluid-Fluid Interfaces With Applications To Droplet Tracking In Contraction Geometries, Ahmad Baniabedalruhman

Dissertations, Master's Theses and Master's Reports - Open

The dynamic meshing procedure in an open source three-dimensional solver for calculating immiscible two-phase flow is modified to allow for simulations in two-dimensional planar and axisymmetric geometries. Specifically, the dynamic mesh refinement procedure, which functions only for the partitioning of three-dimensional hexahedral cells, is modified for the partitioning of cells in two-dimensional planar and axisymmetric flow simulations. Moreover, the procedure is modified to allow for computing the deformation and breakup of drops or bubbles that are very small relative to the mesh of the flow domain. This is necessary to avoid mass loss when tracking small drops or bubbles through …

An Analysis Of Multiplicative Regularization, Elaheh Gorgin

Dissertations, Master's Theses and Master's Reports - Open

Inverse problems arise in many branches of science and engineering. In order to get a good approximation of the solution of this kind of problems, the use of regularization methods is required. Tikhonov regularization is one of the most popular methods for estimating the solutions of inverse problems. This method needs a regularization parameter and the quality of the approximate solution depends on how good the regularization parameter is.

The L-curve method is a convenient parameter choice strategy for selecting the Tikhonov regularization parameter and it works well most of the time. There are some problems in which the L-curve …