#### 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 Advisor

Lorenz, Jens

#### First Committee Member (Chair)

Embid, Pedro

#### Second Committee Member

Hayat, Majeed

#### Third Committee Member

Pereyra, Cristina

#### Language

English

#### Keywords

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

#### Document Type

Dissertation

#### Recommended Citation

Cherepanov, Pavlo. "Shock formation properties of continuum and kinetic models." (2009). http://digitalrepository.unm.edu/math_etds/10