Robust and efficient discontinuous Galerkin methods for under-resolved turbulent incompressible flows

Understand

We present a robust and accurate discretization approach for incompressible turbulent flows based on high-order discontinuous Galerkin methods.

• The DG discretization of the incompressible Navier-Stokes equations uses the local Lax-Friedrichs flux for the convective term, the symmetric interior penalty method for the viscous term, and central fluxes for the velocity-pressure coupling terms.
• Stability of the discretization approach for under-resolved, turbulent flow problems is realized by a purely numerical stabilization approach.
• Consistent penalty terms that enforce the incompressibility constraint as well as inter-element continuity of the velocity field in a weak sense render the numerical method a robust discretization scheme in the under-resolved regime.