Multiphase Flows of N Immiscible Incompressible Fluids: A Reduction-Consistent and Thermodynamically-Consistent Formulation and Associated Algorithm

摘要

We present a reduction-consistent and thermodynamically consistentformulation and an associated numerical algorithm for simulating the dynamicsof an isothermal mixture consisting of $N$ ($N\geqslant 2$) immiscibleincompressible fluids with different physical properties (densities,viscosities, and pair-wise surface tensions). By reduction consistency we referto the property that if only a set of $M$ ($1\leqslant M\leqslant N-1$) fluidsare present in the system then the N-phase governing equations and boundaryconditions will exactly reduce to those for the corresponding $M$-phase system.By theromdynamic consistency we refer to the property that the formulationhonors the thermodynamic principles. Our N-phase formulation is developed basedon a more general method that allows for the systematic construction ofreduction-consistent formulations, and the method suggests the existence ofmany possible forms of reduction-consistent and thermodynamically consistentN-phase formulations. Extensive numerical experiments have been presented forflow problems involving multiple fluid components and large density ratios andlarge viscosity ratios, and the simulation results are compared with thephysical theories or the available physical solutions. The comparisonsdemonstrate that our method produces physically accurate results for this classof problems.