Applied Mathematics Seminar: Numerical schemes for phase field models and its applications to biological systems
March 13, 2020
Speaker: Giordano Tierra-Chica, Assistant Professor, University of North Texas
Abstract: In this talk I will discuss about some PDE systems to represent biological applications that are based on or involve the understanding of the rheology of complex fluids. In particular I will focus on ideas to design efficient and accurate numerical schemes for biofilms and vesicle membranes using phase field models. In fact, I will present an energetic variational approach to model biofilm interaction with fluid flows. The biofilm is assumed an incompressible ternary mixture of viscous and viscoelastic fluids that represents bacteria, EPS and solvent phases. The proposed model satisfies an overall dissipative energy law and is solved with an efficient unconditionally energy-stable splitting scheme that is able to capture large-scale events of biofilm deformation and detachment under different hydrodynamic conditions, results that are qualitatively consistent with laboratory experiments. Moreover, I will also talk about numerical schemes to simulate the deformation of vesicles membranes via minimizing the bending energy.