Worked Out Problem 4: A Transport Problem for the 2D Graetz Flow

In this chapter, we consider a scalar advection-diffusion PDE modeling the Graetz flow problem in a two-dimensional and geometrically parametrized domain. The aim is to obtain efficient evaluations of the thermal field and the output of interest, defined as the integral of the temperature over the outflow boundary. The solution is approximated using reduced order modeling techniques based on the Greedy algorithm and the Successive Constraint 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.