A front tracking algorithm for limited mass diffusion

The advantage of front tracking over capturing methods for the numerical simulation of discontinuity surfaces in fluid flow is to eliminate the numerical diffusion of mass across a fluid interface. For accurate modeling of an interface between miscible fluids, however, physical mass diffusion may be significant, and must be added to the calculation. The main purpose of this paper is to introduce a new front tracking algorithm in which the physical diffusion of mass across a tracked interface is included. The accuracy and convergence properties of this algorithm are discussed. The new algorithm is a subgrid algorithm in the sense that the asymptotic fine grid behavior is identical to conventional untracked (capturing) methods while the coarse grid behavior is improved. It is thus most suitable for modeling small values of physical mass diffusion, for which adequate numerical resolution is computationally demanding. The mixing rates for the 3D Rayleigh-Taylor instability of miscible fluids based on this algorithm agree with experimental values.