In this model, we consider the coupling between the incompressible Navier-Stokes equations and an advection-diffusion equation for the temperature. Streamline diffusion and shock capturing methods are introduced to deal with the numerical instability issues appearing in high Reynolds simulation.
The non-linearity and the complexity of the stabilization operators are treated by a multi-component empirical interpolation method for discrete operators. In this presentation, we will particularly focus on the recent developments in the Feel++ reduced basis framework: we propose a simultaneous construction (SER) for the reduced basis and the affine approximation of the non-linear stabilization operators. As an illustration, we present an application of a cooling system of a printed circuit board with different heat sources.