Publication Date

8-27-2009

Abstract

Continuum mechanics and kinetic theory are two mathematical theories with fundamentally different approaches to the same physical phenomenon. Continuum mechanics together with thermodynamics treat a substance (a gas or a fluid) as a continuous medium and describes the evolution of its macro characteristics via application of the conservation laws to small packets of the substance. Kinetic theory attempts to describe the evolution of the macro parameters by treating a substance as a family of colliding objects. The number of objects must be large enough so a statistical approach can be taken. In this work we introduce a numerical scheme to solve 1-D Bhatnagar-Gross-Krook model equations and examine the formation of a stationary viscous shock. Obtained results are compared to a stationary numerical solution of 1-D Navier-Stokes equation with a similar set of shock forming conditions.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Jens Lorenz

Second Committee Member

Pedro Embid

Third Committee Member

Majeed Hayat

Fourth Committee Member

Maria Cristina Pereyra

Language

English

Keywords

Shock waves--Mathematical models, Viscous flow--Mathematical models, Gas dynamics--Mathematical models, Navier-Stokes equations--Numerical solutions.

Document Type

Dissertation

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