Worked Out Problem 13: Bifurcating Coanda Effect in a Channel

In this chapter, we consider a vector steady nonlinear PDE modeling the bifurcating Coanda effect for an incompressible flow in a two-dimensional channel. The aim is to obtain efficient evaluations of the velocity and pressure fields and the output of interest, defined as the integral of vertical velocity, which is related to the symmetry breaking and non-uniqueness behavior. 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.