Date of Award

Spring 1-1-2017

Document Type

Thesis

Degree Name

Master of Science (MS)

First Advisor

Oleg V. Vasilyev

Second Advisor

John A. Evans

Third Advisor

Michael P. Hannigan

Fourth Advisor

Peter E. Hamlington

Abstract

This study investigates one of the well-known shortcomings of the conservative level set method, namely the ill-defined normal vector. A stabilized formulation is proposed which does not rely on the unit normal vector anymore. Instead, the proposed stabilized conservative level set, SCLS, utilizes a modified normal vector, magnitude of which is unit in the interfacial region of width ε and approaches zero in the far field from the interface. Respective adjustments have been applied on the reinitialization equation to comply with the proposed normal vector. This methodology is general and robust and it is not topology dependent. Since the information in the interfacial region are of a higher interest in comparison to the far field data, SCLS is specially well suited to be used with adaptive mesh refinement, AMR. In this research a general AMR-type approach named Adaptive Wavelet Collocation Method has been utilized, which makes use of wavelets to adapt on meshes in the interfacial region. A number of benchmark numerical problems have been performed to investigate the performance of the stabilized conservative level set approach. SCLS methodology is intended to be a base for simulation of interfacial phenomena, especially multiphase flows.

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