Numerical analysis of a finite element projection-based VMS turbulence model with wall laws

• We develop a stabilized projection-based FE-VMS turbulence model including wall laws.
• We perform the numerical analysis of the model (stability, convergence, error estimates).
• We prove the asymptotic energy balance of the system for slightly smooth flows.
• Smooth flows are solved with optimal accuracy.
• Good accuracy is obtained with benchmark turbulent flow problems on coarse grids.

This paper deals with the numerical analysis of a finite element projection-based VMS turbulence model that includes general non-linear wall laws. Only a single mesh and interpolation operators on a virtual coarser mesh are needed to implement the model. We include a projection-stabilization of pressure to use the same interpolation for velocity and pressure. Good accuracy is obtained with benchmark turbulent flow problems on coarse grids, that justify the interest of this approach. Also, the model solves smooth flows with optimal accuracy.