Numerical diffusion in the FCT algorithm, revisited

Numerical diffusion in a flux-corrected transport (FCT) algorithm embedded in a Navier–Stokes solver (TINY3D) has been analytically and numerically studied for flows where density variations can be neglected. It is found that numerical diffusion can be analytically expressed in a form similar to that of viscous diffusion. The effective total viscosity can be written as an effective viscosity which is the sum of the physical and numerical viscosities. A low-Mach-number laminar boundary-layer flow is used to test the analytical model of numerical diffusion. A series of simulations, in which the amount of numerical diffusion is varied, show results consistent with predictions of boundary-layer theory when the effective total viscosity is used. The minimum required numerical viscosity to meet the linear stability condition and the lower and upper limits of the cell Reynolds number are also derived.