Date of Award
2012-01-01
Degree Name
Master of Science
Department
Mathematical Sciences
Advisor(s)
Son-Young Yi
Abstract
Poroelastic models deal with the coupling of changes in stress and fluid pressure in some porous medium. For physical reasons, some of the coefficients used in the models may have discontinuities. This project focuses on applying the immersed interface method to the one dimensional Biot model, in order to handle these discontinuities. This method is applied on a staggered grid. Using the immersed interface method allows us to alter only a small number of irregular grid points surrounding a discontinuity. For most of the grid points, a standard finite difference method is used. However at the irregular grid points, the method of undetermined coefficients is used to improve the standard approximation. Finally numerical experiments are carried out to confirm an expected convergence rate of O(h + dt).
Language
en
Provenance
Received from ProQuest
Copyright Date
2012
File Size
36 pages
File Format
application/pdf
Rights Holder
Maranda Lee Bean
Recommended Citation
Bean, Maranda Lee, "An Immersed Interface Method for a 1D Poroelasticity Problem with Discontinuous Coefficients" (2012). Open Access Theses & Dissertations. 2041.
https://scholarworks.utep.edu/open_etd/2041