Keywords

crater, rocket exhaust, bearing capacity, soil, finite element method, numerical computation

Abstract

We study numerical methods for solving the nonlinear porous medium and Navier-Lame problems. When coupled together, these equations model the flow of exhaust through a porous medium, soil, and the effects that the pressure has on the soil in terms of spatial displacement. For the porous medium equation we use the Crank-Nicolson time stepping method with a spectral discretization in space. Since the Navier-Lame equation is a boundary value problem, it is solved using a finite element method where the spatial domain is represented by a triangulation of discrete points. The two problems are coupled by using approximations of solutions to the porous medium equation to define the forcing term in the Navier-Lame equation. The spatial displacement solutions can be used to approximate the strain and stress imposed on the soil. An analysis of these physical properties shows whether or not the material ceases to act as an elastic material and instead behaves like a plastic which will tell us if the soil has failed and a crater has formed. Analytical as well as experimental tests are used to find a good balance for solving the porous medium and Navier-Lame equations both accurately and efficiently.

Notes

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Graduation Date

2010

Advisor

Moore, Brian

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0003217

URL

http://purl.fcla.edu/fcla/etd/CFE0003217

Language

English

Release Date

July 2013

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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Included in

Mathematics Commons

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