Date of Award
2018-01-01
Degree Name
Master of Science
Department
Computational Science
Advisor(s)
Xianyi Zeng
Abstract
Modeling tumor growth due to infiltration of immune cells presents several challenges in numerical computations. First, it involves multiple cell species whose total number should be a constant, due to the incompressibility assumption; second, by mapping the Eulerian coordinate of the free-boundary problem onto a fixed logical domain, geometric source terms appear and they need to be addressed properly in numerical methods. In this work, we use a simplified model that contains two species and prescribed infiltration velocity and to show that the conventional finite volume methods fail to preserve the trivial (constant) solutions. To this end, we introduce the totality conservation law (TCL) and the geometric law (GCL) as the two criterions to address the incompressibility and property of preserving constant solutions on changing Eulerian domains, respectively. The classical Godunov-type finite volume methods are enhanced to satisfy these conditions, and performance improvements are verified by numerical tests with arbitrary infiltration velocities.
Language
en
Provenance
Received from ProQuest
Copyright Date
2018-07
File Size
82 pages
File Format
application/pdf
Rights Holder
Mashriq Ahmed Saleh
Recommended Citation
Saleh, Mashriq Ahmed, "Mathematical Modeling Of Tumor Growth For Free-Boundary Problem By Enhanced Finite Volume Method" (2018). Open Access Theses & Dissertations. 1537.
https://scholarworks.utep.edu/open_etd/1537