Incompressible Multiphase Flows: Physical Formulation and Numerical Algorithm

Listed in Datasets

By Suchuan Dong

Purdue University

We present a family of thermodynamically consistent physical formulation and efficient numerical algorithm for simulating the mixture of N (N >= 2) immiscible incompressible fluids with given densities, dynamic viscosities and...

Additional materials available

Version 1.0 - published on 07 Apr 2015 doi:10.4231/R7J9649P - cite this Archived on 25 Oct 2016

Licensed under Attribution-NonCommercial-No Derivs 3.0 Unported



We present a family of physical formulations, and a  numerical algorithm, based on a class of general order parameters for simulating the motion of a mixture of N (N >= 2) immiscible incompressible fluids with given densities, dynamic viscosities, and pairwise surface tensions. The N-phase formulations stem from a phase field model we developed in a recent work based on the conservations of mass/momentum, and the second law of thermodynamics. The introduction of general order parameters leads to an extremely strongly-coupled system of (N-1) phase field equations. On the other hand, the general form enables one to compute the N-phase mixing energy density coefficients in an explicit fashion in terms of the pairwise surface tensions. We show that the increased complexity in the form of the phase field equations associated with general order parameters in actuality does not cause essential computational difficulties. Our numerical algorithm reformulates the (N-1) strongly-coupled phase field equations for general order parameters into 2(N-1) Helmholtz-type equations that are completely de-coupled from one another. This leads to a computational complexity comparable to that for the simplified phase field equations associated with certain special choice of the order parameters. We demonstrate the capabilities of the method developed herein using several test problems involving multiple fluid phases and large contrasts in densities and viscosities among the multitude of fluids. In particular, by comparing simulation results with the Langmuir-de Gennes theory of floating liquid lenses we show that the method using general order parameters produces physically accurate results for multiple fluid phases. 

Cite this work

Researchers should cite this work as follows:



Data files for paper "S. Dong, Physical formulation and numerical algorithm for simulating N immiscible incompressible fluids involving general order parameters, Journal of Computational Physics, 283, 98-128, 2015".

The Purdue University Research Repository (PURR) is a university core research facility provided by the Purdue University Libraries, the Office of the Executive Vice President for Research and Partnerships, and Information Technology at Purdue (ITaP).