Modeling studies and numerical analyses of coupled PDEs system in electrohydrodynamics

MODELING STUDIES AND NUMERICAL ANALYSES OF COUPLED PDES SYSTEM IN ELECTROHYDRODYNAMICS by Yuzhou Sun Dr. Pengtao Sun, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas, USA Electrohydrodynamics (EHD) is the term used for the hydrodynamics coupled with electrostatics, whose governing equations consist of the electrostatic potential (Poisson) equation, the ionic concentration (Nernst-Planck) equations, and NavierStokes equations for an incompressible, viscous dielectric liquid. In this dissertation, we focus on a specific application of EHD fuel cell dynamics in the field of renewable and clean energy, study its traditional model and attempt to develop a new fuel cell model based on the traditional EHD model. Meanwhile, we develop a series of efficient and robust numerical methods for these models, and carry out their numerical analyses on the approximation accuracy. In particular, we analyze the error estimates of finite element method for a simplified 2D isothermal steady state two-phase transport model of Proton Exchange Membrane Fuel Cell (PEMFC) as well as its transient version. On the aspect of hydrodynamics arising in the fuel cell system, the fluid flow through the open channels and porous media at the same time, both Navier-Stokes equations and Darcys law are involved in the fluid domains, leading to a Navier-Stokes-Darcy coupling problem. In this dissertation, we study a one-continuum model approach, so-called Brinkman model, to overcome this problem iii in a more efficient way. To develop a new fuel cell model based on EHD theory, in addition to the two-phase transport model of fuel cells, we carry out numerical analyses for Poisson-Nernst-Planck (PNP) equations using both standard FEM and mixed FEM, which are the essential governing equations involved by EHD model. Finally, we are able to further extend the traditional fuel cell model to more general cases in view of EHD characteristics, and develop a new fuel cell model by appropriately combining PNP equations with the traditional fuel cell model. We conduct the error analysis for PNP-Brinkman system in this dissertation.