Degree Type

Thesis

Date of Award

2017

Degree Name

Master of Science

Department

Mathematics

Major

Applied Mathematics

First Advisor

Jue Yan

Abstract

In this thesis, we discuss first and second order finite volume methods to solve the one dimensional compressible Navier-Stokes equations. We prove the first order finite volume method preserves positivity for the density and pressure. We carry out a sequence of numerical tests including the famous Shock tube problem, extreme Riemann double rarefaction wave case, etc. For those cases with very low density, our scheme performed well and the density and pressure remain positive throughout the domain. We further consider to extend the positivity preserving discussion to second order finite volume methods.

Copyright Owner

Heather Muchowski

Language

en

File Format

application/pdf

File Size

42 pages

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