Latest developments

Our latest results break ground in turbulent aerodynamics simulation using finite element methods! Together with my partners Ernesto Castillo, Alejandro Aguirre and Diego Escobar from USACH (Chile), we are using efficient variational multiscale (VMS) methods with dynamic subscales as a very robust alternative to more traditional LES techniques. The mechanism works analogously to a filter: the FE mesh resolves large flow structures (coarse scale), while orthogonal projections guarantee that the subscales only carry the fine corrections ("missing details"). This clean separation avoids redundancy, prevents spurious feedback between scales, and ensures that the stabilisation terms act only where needed. As a result, the method remains stable even with unbalanced space-time resolutions, and the consistency error is of optimal order. 

Our simulations include high-speed incompressible aerodynamics (Re = 1 million) around a Formula 1 car model, where we are able to not only achieve highly stable results, but also recover the theoretical slopes of the Kolmogorov cascade. Below are some of our latest results, but a full preprint should be coming out in the next couple of weeks!