An iterative split scheme for steady flows with heterogeneous viscosity

Abstract

This paper proposes a numerical scheme for the approximation of the solution of the Stokes or steady Navier–Stokes system for fluids with heterogeneous viscosity (generic bounded viscosity or shear thinning fluids). The scheme is based on a velocity–pressure splitting resembling a Uzawa approach combined with a grad-div stabilizing term. We establish the validity, convergence and a priori estimates for this strategy. A simpler mixed approach is also presented and studied. Numerical tests using a manufactured solution are provided, giving estimates for the accuracy order and sensitivity to the stabilizing coefficient. For more realistic numerical experiments, we present results for the lid-driven cavity.