A mimetic finite difference method for Large Eddy Simulation of incompressible flow
Tuesday 9th November 2010
Abba', A.; Bonaventura, L.
A finite difference discretization of the three-dimensional, incompressible Navier-Stokes equations is presented, based on finite difference operators that satisfy discrete analogs of some basic calculus identities. These mimetic properties yield a numerical method for which a discrete form of the vorticity equation can be derived naturally from the discrete momentum equation, by application of the mimetic rotation operator. As a result,a discrete approximation of vorticity is exactly preserved, for inviscid flows, independently of the mesh size. The vorticity preservation property guarantees that no spurious vorticity is generated by the nonlinear advective terms in absence of viscosity. A mimetic discretization of the viscous terms and an appropriate treatment for rigid wall boundary conditions are also proposed. The relationship of this approach to other similar techniques is discussed. The proposed method is validated on several idealized test cases for laminar incompressible flow, in which it is compared to a widely used finite difference discretization. The method is then applied to Large Eddy Simulation of incompressible flow, demonstrating the advantages of the inherentconservation properties in a comparison with experimental data and DNS results especially when strong vorticity production takes place at the boundaries.