Discrete Exterior Calculus Discretization of Axisymmetric Incompressible Two-Phase Navier-Stokes Equations with a Conservative Phase Field Method

doi:10.1007/s42967-025-00483-5

Abstract

Abstract: We present a discrete exterior calculus (DEC) based on the discretization scheme for axisymmetric incompressible two-phase flows, in which the previous work [39] is extended to its axisymmetric version. We first transform the axisymmetric two-phase incompressible Navier-Stokes (NS) equations and the auxiliary conservative phase field (PF) equation into the exterior calculus framework using differential forms and exterior operators. Discretization of these exterior calculus equations is obtained using discrete differential forms and exterior operators. The PF variable, used to capture the interface between the two phases, varies from zero to unity, and preserving these bounds is desirable. Several verification and validation tests are presented to numerically confirm mass conservation, solution boundedness, and convergence properties. Various axisymmetric two-phase flow simulations, including a drop oscillation, a bubble bursting, a rising bubble, and a drop merger, with large density and viscosity ratios and surface tension, demonstrate the excellent performance of DEC dealing with axisymmetric two-phase flows.

Key words: Discrete exterior calculus (DEC), Axisymmetric multiphase flow, Phase field (PF) method, Incompressible Navier-Stokes (NS) equations

CLC Number:

65K05
90C46

Minmiao Wang, Wei Gao, Matteo Parsani. Discrete Exterior Calculus Discretization of Axisymmetric Incompressible Two-Phase Navier-Stokes Equations with a Conservative Phase Field Method[J]. Communications on Applied Mathematics and Computation, 2026, 8(3): 972-1004.

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