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Numerical analysis of a finite element projection-based VMS turbulence model with wall laws. (English) Zbl 1423.76218

Summary: 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.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76F06 Transition to turbulence
76F65 Direct numerical and large eddy simulation of turbulence

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