A synchronous and iterative flux-correction formalism for coupled transport equations

Many problems of fluid dynamics involve the coupled transport of several, density-like, dependent variables (for instance, densities of mass and momenta in elastic flows). In this paper, a conservative and synchronous flux-corrected transport (FCT) formalism is developed which aims at a consistent transport of such variables. The technique differs from traditional FCT algorithms in two respects, First, the limiting of transportive fluxes of the primary variables (e.g., mass and momentum) does not derive from smooth estimates of the variables, but it derives from analytic constraints implied by the Lagrangian form of the governing continuity equations, which are imposed on the specific mixing ratios of the variables (e.g., velocity components). Second, the traditional FCT limiting based on sufficiency conditions is augmented by an iterative procedure which approaches the necessity requirements. This procedure can also be used in the framework of traditional FCT schemes, and a demonstration is provided that it can significantly reduce some of the pathological behaviors of FCT algorithms. Although the approach derived is applicable to the transport of arbitrary conserved quantities, it is particularly useful for the synchronous transport of mass and momenta in elastic flows, where it assures intrinsic stability of the algorithm regardless of the magnitude of the mass-density variable. This latter property becomes especially important in fluids with large density variations, or in models with a material ''vertical'' coordinate (e.g., geophysical hydrostatic stratified flows in isopycnic/isentropic coordinates), where material surfaces can collapse to zero-mass layers admitting, therefore, arbitrarily large local Courant numbers. (C) 1996 Academic Press, Inc.