A simple approach to discretize the viscous term with spatially varying (eddy-)viscosity

Abstract

A simple approach to discretize the viscous dissipation term in the incompressible Navier–Stokes equations with spatially varying viscosity is presented. Unlike the case where the viscosity remains constant, its discretization may be quite cumbersome especially for high-order staggered formulations. To circumvent this problem, we propose an alternative form of the viscous term whose discretization is straightforward. Notice that this approach is also suitable for eddy-viscosity models for Large-Eddy Simulation. Moreover, since it is based on already available operators, it can be easily implemented on any structured or unstructured code. The (supra)convergence of the method is numerically shown on both a fourth-order Cartesian staggered and an unstructured collocated formulation.