A high order splitting scheme for the Navier–Stokes equations with variable viscosity Original Research Article

The objective of this paper is to extend the splitting scheme of Karniadakis et al. (1991) to temporally and spatially varying viscosity, while retaining the decoupling of the viscous term. The derivation of the algorithm and a simplified von Neumann stability analysis for the one-dimensional diffusion equation is presented, demonstrating that for a linear diffusion equation, the scheme is unconditionally stable if the implicit part of the viscosity is larger than the explicit part.