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Course Description: Modeling of transport phenomena from governing physical principles (e.g. fluid flow) and numerical analysis of the underlying differential equations have a broad spectrum of applications ranging from biomedicine, engineering design and simulation, aerodynamics, weather forecasting to animated motion pictures. Topics covered will emphasize on a collective learning of physical phenomena and theoretical models that govern fluid flow, mathematical formulation, numerical analysis and visualization of fluid flow. Particular emphasis will be on mathematical development of finite-element methods for incompressible Navier-Stokes equations governing fluid flow in a non-moving domain. Class projects will be structured to aid learning key theoretical concepts and techniques such as implementation of numerical techniques and simulation of fluid flow, smoke and fire or a similar transport problem related to students’ research interests. Specific topics that will be covered are: 1) A general form of differential equation governing transport phenomena; 2) strong form of the incompressible Navier-Stokes equations governing fluid flow; 3) stability and oscillatory-solution issues with Galerkin finite element; 4) streamline-upwind/Petrov-Galerkin (SUPG) formulation; 5) residual-based variational multiscale formulation (RBVMS); 6) modeling laminar and turbulent flows; 7) finite element formulation of water, fire, smoke and viscous fluids; 8) error analysis; and 9) students will complete a project work in their area of interest / research. PhD students registering at the 8000 level will exhibit deeper understanding by submitting / presenting a research paper based on their projects or on more advanced topics in modeling transport phenomena.


syllabi, syllabus, engineering, electrical engineering, fluid flow, transport phenomena, numerical analysis, differential equations, Navier-Stokes equations