Discretisation of diffusive fluxes on hybrid grids

The main approaches of discretising the viscous operator of fluid flow on hybrid meshes are analysed for accuracy, consistence, monotonicity and sensitivity to mesh quality. As none of these approaches is fully satisfactory, a novel method using an approximated finite element approach is presented and analysed. The methods are compared for the linear heat equation and the Navier-Stokes equations. While the novel approximated finite-element method performs significantly better for the linear heat equation, a stabilised edge-based method performs equally well for the considered test-cases for the Navier-Stokes equations.