A consistent and conservative model and its scheme for -phase--component incompressible flows
arXiv:2101.04252 · doi:10.1016/j.jcp.2021.110229
Abstract
In the present work, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure phase, each pair of phases is immiscible, and components are dissolvable in some specific phases. The model is developed based on the multiphase Phase-Field model including the contact angle boundary condition, the diffuse domain approach, and the analyses on the proposed consistency conditions for multiphase and multicomponent flows. The model conserves the mass of individual pure phases, the amount of each component in its dissolvable region, and thus the mass of the fluid mixture, and the momentum of the flow. It ensures that no fictitious phases or components can be generated and that the summation of the volume fractions from the Phase-Field model is unity everywhere so that there is no local void or overfilling. It satisfies a physical energy law and it is Galilean invariant. A corresponding numerical scheme is developed for the proposed model, whose formal accuracy is 2nd-order in both time and space. It is shown to be consistent and conservative and its solution is demonstrated to preserve the Galilean invariance and energy law. Numerical tests indicate that the proposed model and scheme are effective and robust to study various challenging multiphase and multicomponent flows.
References in corpus (10)
- A volume-of-fluid method for interface-resolved simulations of phase-changing two-fluid flows
- Coalescence of surfactant-laden drops by Phase Field Method
- Multiphase Flows of N Immiscible Incompressible Fluids: A Reduction-Consistent and Thermodynamically-Consistent Formulation and Associated Algorithm
- Coupled THINC and level set method: a conservative interface capturing scheme with arbitrary-order surface representations
- Wall-bounded multiphase flows of N immiscible incompressible fluids: consistency and contact-angle boundary condition
- A consistent and conservative Phase-Field method for multiphase incompressible flows
- Physical Formulation and Numerical Algorithm for Simulating N Immiscible Incompressible Fluids Involving General Order Parameters
- Multiphase Allen-Cahn and Cahn-Hilliard Models and Their Discretizations with the Effect of Pairwise Surface Tensions
- A consistent and conservative volume distribution algorithm and its applications to multiphase flows using Phase-Field models
- Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries