Fabrice Babik

Discretization of the viscous dissipation term with the MAC scheme

We propose a discretization for the MAC scheme of the viscous dissipation term τ(u) : Δu (where τ(u) stands for the shear stress tensor associated to the velocity field u), which is suitable to obtain an unconditionally stable scheme for the compressible Navier-Stokes equations. It is also shown, in some model cases, to ensure the strong convergence in L1 of the dissipation term.

A Staggered Scheme with Non-conforming Refinement for the Navier-Stokes Equations

We propose a numerical scheme for the incompressible Navier-Stokes equations. The pressure is approximated at the cell centers while the vector valued velocity degrees of freedom are localized at the faces of the cells. The scheme is able to cope with unstructured non-conforming meshes, involving hanging nodes. The discrete convection operator, of finite volume form, is built with the purpose to obtain an \(L^2\)-stability property, or, in other words, a discrete equivalent to the kinetic energy identity. The diffusion term is approximated by extending the usual Rannacher-Turek finite element to non-conforming meshes. The scheme is first order in space for energy norms, as shown by the numerical experiments.