On Conservative Smoothers for Turbulent Convection: an Alternative Simulation Shortcut

Most turbulent flows can not be computed directly from the Navier-Stokes equations, because they possess far too many scales of motion. The computationally almost numberless small scales result from the nonlinear convective term which allows for the transfer of energy from scales as large as the flow domain to the smallest scales that can survive viscous dissipation. In the quest for a simulation shortcut, we propose to smooth the convective term in such a way that the symmetries that yield the invariance of the energy, enstrophy (in 2D) and helicity are preserved. This requirement yields a class of conservative smoothers. The numerical algorithm used to solve the governing equations also preserves the symmetries and is therefore well-suited to test the proposed simulation shortcut. The simulation shortcut is successfully tested for turbulent channel flow (Reτ = 180). NAVIER-STOKES EQUATIONS AND TURBULENCE The Navier-Stokes equations provide an appropriate model for turbulent flow. In the absence of compressibility (∇ · u = 0), the equations are ∂tu+ C(u, u) +D(u) +∇p = 0 (1) where the nonlinear, convective term is given by