Stabilized formulations for incompressible flows with thermal coupling

We present applications of the stabilized finite element formulations developed for incompressible flows with thermal coupling to 2D and 3D test problems. The stabilized formulations are based on the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/ Petrov-Galerkin stabilizations and are supplemented with discontinuity capturing (DC), including the discontinuity-capturing directional dissipation. The stabilization and DC parameters associated with these formulations are also presented. The coupled fluid mechanics and temperature equations are solved with a direct coupling technique. The test problems computed include 2D and 3D natural convection, as well as a simplified 3D model of air circulation in a small data center.