Parallel and adaptive VMS finite elements formulation for aerothermal problems

In this work, we develop a new mesh adaptation technique to solve the thermal problem of the impingement jet cooling. To do so, we start by proposing a subscales error estimator computed with bubble functions to locate and evaluate the PDE-dependent approximation error. Then, two new metric tensors Hiso and Hanisonew based on the subscales error estimator are proposed for respectively isotropic and anisotropic mesh adaptation. For anisotropic mesh adaptation in particular, we combine the coarse scales anisotropic interpolation error indicator with the subscales error estimator allowing us to take into account the anisotropic variations of the solution but also the sub-grid information. Finally, a special focus is put on the ability to strongly couple the anisotropic multiscale error estimator with parallel computation in order to achieve an efficient parallel adaptive framework. The results show that the resulting meshes allow to capture the turbulently generated flow specificities of the impingement jet cooling and in particular, the secondary vortexes.