  The operator splitting approach applied to the Navier-Stokes equations, gave
rise to various numerical methods for the simulations of the dynamics of
fluids. The separate work of Chorin and Temam on this subject gave birth to the
so-called projection methods. The basic projection schemes, either the
incremental or non-incremental variant (see [1]) induces an artificial Neumann
boundary condition on the pressure. By getting rid of this boundary condition
on the pressure, the so-call rotational incremental pressure-correction scheme
as proposed by Timmermans et al. [2] for Newtonian fluids with constant
viscosity gives a consistent equation for the pressure. In this work we propose
a family of projection methods for generalized Newtonian fluids based on an
extension of the rotational projection scheme. Called shear rate projections,
these methods produces consistent pressure when applied to generalized
Newtonian fluids. Accuracy of the methods will be illustrated using a
manufactured solution. Numerical experiments for the flow past a cylinder, with
a Carreau rheological model, will also be presented.
