Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows

Research output: Contribution to journalArticle

Abstract

A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn–Hilliard and Allen–Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.

Original languageEnglish
Pages (from-to)64-97
Number of pages34
JournalJournal of Computational Physics
Volume356
DOIs
Publication statusPublished - 2018 Mar 1

Fingerprint

two phase flow
brackets
Two phase flow
preserving
Numerical methods
formulations
Difference equations
Finite difference method
Kinetic energy
Viscosity
Derivatives
energy
difference equations
budgets
vorticity
kinetic energy
Experiments
viscosity
tubes
formalism

Keywords

  • Bracket formulation
  • Diffuse interface model
  • Discrete variational derivative method
  • Mimetic finite difference method
  • Two-phase flow

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

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title = "Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows",
abstract = "A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn–Hilliard and Allen–Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.",
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