Semi-Lagrangian discretization of the upper-convective derivative in Non-Newtonian fluid flow



Non-Newtonian fluid flow is governed by the Navier-Stokes equations with an additional source term resulting from Non-Newtonian stresses. The Non-Newtonian stresses evolve along particle paths according to an evolution equation. The temporal derivative in this case is the upper convected derivative. We describe a semi-Lagrangian discretization of the upper convected derivative. Numerical results for the flow over a contraction are given. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)