Preconditioning the Incompressible Navier-Stokes Equations with Variable Viscosity

Abstract

This paper deals with preconditioners for the iterative solution of the discrete Oseen problem with variable viscosity. The motivation of this work originates from numerical simulations of multiphase flow, governed by the coupled Cahn-Hilliard and incompressible Navier-Stokes equations. The impact of variable viscosity on some known preconditioning technique is analyzed. Theoretical considerations and numerical experiments show that some broadly used preconditioning techniques for the Oseen problem with constant viscosity are also efficient when the viscosity is varying.