A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:360

Article

Joshi, Vaibhav¹  Jaiman, Rajeev K.¹ 

[1] Natl Univ Singapore, Dept Mech Engn, Singapore 119077, Singapore

关键词: Mass conservative;    Energy stable;    Positivity preserving;    Allen-Cahn phase-field;    Two-phase flows;    Wave-structure interaction;   

DOI  :  10.1016/j.jcp.2018.01.028

来源: Elsevier

【 摘 要 】

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two-and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction. (c) 2018 Elsevier Inc. All rights reserved.

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