Keywords

Numerical methods, darcy flow, porous media, crater formation, domain decomposition, alternating direction implicit, piecewise hermite bicubics

Abstract

Physical lab experiments have shown that the pressure caused by an impinging jet on a granular bed has the potential to form craters. This poses a danger to landing success and nearby spacecraft for future rocket missions. Current numerical simulations for this process do not accurately reproduce experimental results. Our goal is to produce improved simulations to more accurately and effi- ciently model the changes in pressure as gas flows through a porous medium. A two-dimensional model in space known as the nonlinear Porous Medium Equation as it is derived from Darcy’s law is used. An Alternating-Direction Implicit (ADI) temporal scheme is presented and implemented which reduces our multidimensional problem into a series of one-dimensional problems. We take advantage of explicit approximations for the nonlinear terms using extrapolation formulas derived from Taylor-series, which increases efficiency when compared to other common methods. We couple our ADI temporal scheme with different spatial discretizations including a second-order Finite Difference (FD) method, a fourth-order Orthogonal Spline Collocation (OSC) method, and an Nth-order Chebyshev Spectral method. Accuracy and runtime are compared among the three methods for comparison in a linear analogue of our problem. We see the best results for accuracy when using an ADI-Spectral method in the linear case, but discuss possibilities for increased effi- ciency using an ADI-OSC scheme. Nonlinear results are presented using the ADI-Spectral method and the ADI-FD method.

Notes

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Graduation Date

2013

Semester

Fall

Advisor

Moore, Brian

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0005017

URL

http://purl.fcla.edu/fcla/etd/CFE0005017

Language

English

Release Date

12-15-2016

Length of Campus-only Access

3 years

Access Status

Masters Thesis (Open Access)

Subjects

Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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