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March 2020

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12
Mar

[CANCELED] Department Colloquium: The Fourier pseudo-spectral numerical schemes for nonlinear PDEs and their stability

Conference/Seminar

Speaker: Cheng Wang, Professor, Department of Mathematics, University of Massachusetts Dartmouth

Abstract: The Fourier pseudo-spectral numerical schemes are considered for nonlinear partial differential equations (PDE). Stability and convergence analysis are analyzed in detail, such as viscous Burgers' equation and incompressible fluid equations. Related applications to the incompressible quasi-geostrophic equation will also be addressed, in both 2-D and 3-D, for smooth and vortex sheet initial data. In addition, high order time-stepping schemes (up to fourth-order accuracy order) will be explored in detail. Unconditional stability is established for the implicit time-stepping algorithms.

3:30 pm - 4:30 pm | Animal Science |
13
Mar

[CANCELED] Applied Mathematics Seminar: Numerical schemes for phase field models and its applications to biological...

Conference/Seminar

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.

3:30 pm - 4:30 pm | Animal Science |
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