Worked Out Problem 14: Unsteady Navier-Stokes Equations for Vortex Shedding Behind a Cylinder

In this chapter, we consider a vector time-dependent nonlinear PDE modeling the unsteady Navier-Stokes system for an incompressible flow in a two-dimensional domain with a cylindrical obstacle. The aim is to obtain efficient evaluations of the velocity and pressure fields and the output of interest, defined as the average of the solution over the whole domain for the last time step. The solution is approximated using reduced order modeling techniques based on the POD-Galerkin method. The problem is described by presenting the physical domain, the goal, the parametrization, the boundary conditions, the governing PDE, and the corresponding weak formulation with its affine decomposition. Numerical results show the performance of the reduced approach with respect to the high-fidelity discretization, the quantity of interest, and the speedup. We provide the links to the source code, to the Jupyter notebook, and to the web-server ARGOS.