Compressible flows are present nowadays in many topics of interest. For example, the performance of gas turbines — which are widely used in energy production and in aircraft and shift propulsion — is clearly related to the irreversibilities (shock waves, stall, etc.) experimented by the fluid at the compression and expansion stages. In aeronautics, an effort is being made to reduce fuel consumption and to develop new engines and aircrafts suitable for higher speed flights. Finally, in civil engineering, it is primordial to build factories and industrial warehouses as resistant to explosions (i.e., shock waves) las possible.

The equations that govern compressible flows are known since the mid-twentieth century, but their analytical resolution still remains a challenge for the scientific community. Hence, it is primordial to develop accurate and efficient numerical schemes to approach their study. In this group, we develop finite element methods of Lagrange–Galerkin type, which are characterized for discretizing the convective terms of the equations along the trajectories of the fluid particles, allowing this way for better stability properties. Currently, our work is focused on the following lines:

• conservative schemes,
• discontinuity-capturing operators,
• high-order discretizations on unstructured triangular meshes,
• hp anisotropic mesh refinement.

Researchers: Manuel Colera Rico, Jaime Carpio Huertas.
Collaborators: R. Bermejo. P. Galán del Sastre, L. Saavedra (UPM), Vít Dolejší (Charles University).

Relevant publications: