THE MODIFIED EQUATION APPROACH TO FLUX-CORRECTED TRANSPORT

For convective problems, the "modified equation" can be considered as the actual partial differential equation solved by a given numerical scheme using finite differences. Such an expression characterizes the dissipative and dispersive properties of the scheme. Adjusting the parameters of flux-corrected-transport (FCT) algorithms to cancel the successive truncation terms in the modified equation can be used in place of Fourier analysis when the velocity is no longer constant and uniform. This technique is used to propose a time-centered FCT algorithm in which diffusion/antidiffusion coefficients are velocity gradient dependent and which has reduced diffusion and noise level. © 1990.