Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities
arXiv:2408.04371 · doi:10.1016/j.jcp.2024.113331
Abstract
In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{ü}n (AGG) model, which is a thermodynamically consistent phase field model of two-phase incompressible flows with different densities. Both schemes are decoupled, linear, second-order in time, and the numerical implementation turns out to be straightforward. The first scheme solves the Navier-Stokes equations in a saddle point formulation, while the second one employs the artificial compressibility method, leading to a fully decoupled structure with a time-independent pressure update equation. In terms of computational cost, only a sequence of independent elliptic or saddle point systems needs to be solved at each time step. At a theoretical level, the unique solvability and unconditional energy stability (with respect to a modified energy functional) of the proposed schemes are established. In addition, comprehensive numerical simulations are performed to verify the effectiveness and robustness of the proposed schemes.
References in corpus (12)
- Two-phase binary fluids and immiscible fluids described by an order parameter
- A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation
- Improving the Accuracy and Consistency of the Scalar Auxiliary Variable (SAV) Method with Relaxation
- A generalized SAV approach with relaxation for dissipative systems
- Multiphase Flows of N Immiscible Incompressible Fluids: A Reduction-Consistent and Thermodynamically-Consistent Formulation and Associated Algorithm
- An Unconditionally Energy-Stable Scheme Based on an Implicit Auxiliary Energy Variable for Incompressible Two-Phase Flows with Different Densities Involving Only Precomputable Coefficient Matrices
- An embedded variable step IMEX scheme for the incompressible Navier-Stokes equations
- A Stable Parametric Finite Element Discretization of Two-Phase Navier--Stokes Flow
- An energy-stable Smoothed Particle Hydrodynamics discretization of the Navier-Stokes-Cahn-Hilliard model for incompressible two-phase flows
- Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes
- A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes
- A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow