A staggered projection scheme for viscoelastic flows

We develop a numerical scheme for the flow of viscoelastic fluids, including OldroydB and FENE-CR constitutive models. The space discretization is staggered, using either Marker-And-Cell (MAC) structured nonuniform grids, or Rannacher Turek (RT) nonconforming low-order finite element approximation general quandrangular hexahedral meshes. time uses fractional-step algorithm where solution Navier-Stokes equations first obtained by projection method then transport-reaction equation conformation tensor solved volume scheme. In order to obtain consistency, divergence elastic part stress in momentum balance derived weak form MAC For stability accuracy purposes, split into pure convection steps, with change variable log-conformation tensor, reaction step, which consists solving one ODE per cell via an Euler local sub-cycling. Numerical computations lid-driven cavity at Weissenberg numbers above around confined cylinder confirm efficiency