Date of Award
8-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Lea Jenkins
Committee Member
Vince Ervin
Committee Member
Timo Heister
Committee Member
Sibusiso Mabuza
Abstract
We consider a nonlinear transport problem to model the chromatography process of high-capacity multimodal membranes. Robust and efficient algorithms that simulate these bioseparation processes are critical to developing therapeutics for various chronic illnesses and infectious diseases. However, much of the current methodology focuses on stabilization and linearization techniques, often implementing low-order time-discretizations and linearized adsorption, resulting in inefficiencies and inaccuracies in the numerical solution. Utilizing Rothe's method, we develop various time-discretization schemes coupled with the finite element method to solve the fully implicit problems. Stability and solvability results are presented for several methods. Through multiple high-level software implementations paired with national laboratory solvers, we verify a priori error estimates and generate breakthrough curves to test the experimental validity of the numerical solutions. We also test our methods by sweeping over the feasible set of adsorption parameters. Our results indicate that these methods have significantly improved the current simulation framework to model downstream filtration processes.
Recommended Citation
Butterworth, Evan D., "Accurate Temporal Integration Schemes for Nonlinear Adsorption Problems" (2025). All Dissertations. 4023.
https://open.clemson.edu/all_dissertations/4023
Author ORCID Identifier
https://orcid.org/0000-0002-6153-2938