This course covers finite element-based approaches to solve problems in fluid mechanics including the Navier-Stokes equations and its variants. Emphasis is placed on variational multiscale and stabilized methods. Experience in numerical methods and programming is assumed. Different transport equations are considered starting from an advection-diffusion equation. Issues concerning implementation are also discussed pertaining to the numerical formulation, stabilizaton parameter, time integrator, nonlinear equation iterator, finite element assembly, boundary conditions, and linear solver.
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