Date of Degree

6-2016

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Tobias Schaefer

Advisor

Jesenko Vukadinovic

Committee Members

Jozef Dodziuk

Olympia Hadjiliadis

Subject Categories

Partial Differential Equations

Keywords

Advection-Diffusion, Multiple Scales, Averaging

Abstract

Many models for physical systems have dynamics that happen over various different time scales. For example, contrast the everyday waves in the ocean with the larger, slowly moving global currents. The method of multiple scales is an approach for approximating the solutions of differential equations by separating out the dynamics at slower and faster time scales. In this work, we apply the method of multiple scales to generic advection-diffusion equations (both linear and non-linear, and in arbitrary spatial dimensions) and develop a method for 'averaging out' the faster scale phenomena, giving us an 'effective' solution for the slower scale dynamics. Numerical results are then obtained to confirm the effectiveness of this technique.

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