Discrete exterior calculus discretization of two-phase incompressible Navier-Stokes equations with a conservative phase field method

Minmiao Wang, Pankaj Jagad, Anil N. Hirani, Ravi Samtaney

Research output: Contribution to journalArticlepeer-review


We present a discrete exterior calculus (DEC) based discretization scheme for incompressible two-phase flows. Our physically-compatible exterior calculus discretization of single phase flow is extended to simulate immiscible two-phase flows with discontinuous changes in fluid properties such as density and viscosity across the interface. The two-phase incompressible Navier-Stokes equations and conservative phase field equation for interface capturing are first transformed into the exterior calculus framework. The discrete counterpart of these smooth equations is obtained by substituting with discrete differential forms and discrete exterior calculus operators. We prove the boundedness of the method for the forward Euler and predictor-corrector time integration schemes in the DEC framework. With a proper choice of two free parameters, the scheme remains phase field bounded without the requirement of any ad hoc mass redistribution. We verify the scheme against several standard test cases (for interface capturing) comprising not only the flat domains but also the curved domains, leveraging the advantage that DEC operators are independent of the coordinate system. The results show excellent properties of boundedness, mass conservation and convergence. Moreover, we demonstrate the ability of the scheme to handle large density and viscosity ratios as well as surface tension in the simulation of various two phase flow physical phenomena on flat or curved surfaces.
Original languageEnglish (US)
Pages (from-to)112245
JournalJournal of Computational Physics
StatePublished - Jun 1 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-06-07
Acknowledged KAUST grant number(s): URF/1/3723-01-01
Acknowledgements: This research was supported by the KAUST Office of Sponsored Research under Award URF/1/3723-01-01. We thank Nikolas Wojtalewicz (UIUC) for discussions on the boundedness analysis in Section 2.4 for the case of the Euler method. Nikolas Wojtalewicz independently arrived at the same conclusions. We thank Mamdouh Mohamed (Cairo University, Egypt) for discussions.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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