FINITE-ELEMENT IMPLEMENTATION AND VERIFICATION OF COMPLEX FLUID MODELS BASED ON EVOLVING NATURAL CONFIGURATIONS, MOTIVATED BY STUDIES OF BLOOD

Open Access
Author:
Awadelkarim, Amel Osama
Graduate Program:
Engineering Science and Mechanics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
August 14, 2017
Committee Members:
  • Francesco Costanzo, Thesis Advisor
Keywords:
  • blood
  • fluid mechanics
  • COMSOL Multiphysics
  • continuum mechanics
  • arbitrary-Lagrangian-Eulerian
  • Method of Manufactured Solutions
  • clotting
  • lysis
  • modeling
  • viscoelastic fluids
  • finite element
  • complex fluids
  • verification
  • thermodynamics
  • natural configuration
  • Oldroyd-B fluid
Abstract:
The ability to model the flow of blood along with its concurrent capacity for clotting and lysis can greatly accelerate the development and deployment of many clinical applications. Examples of these range from novel surgical therapies for acute ischemic stroke to intra-operative pharmacological interventions for the prevention of massive coagulation or hemorrhage in liver transplantation. In this study, a specific fully-coupled model is selected from the literature for the flow, clotting, and lysis of blood. A new approach is then proposed for the finite element method (FEM) implementation of this model. Specifically, a reduced model is first considered, limited to the mere mechanical response of an incompressible (viscoelastic) Oldroyd-B fluid. For this model, Eulerian, Lagrangian, and arbitrary Lagrangian-Eulerian (ALE) finite element (FE) implementations are considered. Subsequently, the model is expanded to include reaction and diffusion concurrent with advection, which is necessary to model the chemistry of blood clotting and lysis that can take place during blood flow. The proposed FEM scheme is then extended to be applicable to the fully-coupled model. COMSOL Multiphysics® has been used as the programming environment for the FEM implementation. The accuracy of the proposed implementations has been assessed using the method of manufactured solutions (MMS). A convergence analysis is performed to observe the dependence of the error in the numerical solutions upon refinement of the mesh. Finally, we propose sources of error in the solver and discuss future work for the use of the proposed formulation in physiologically relevant applications.