Mass Conservative and Energy Stable Finite Difference Methods for the Quasi-incompressible Navier-Stokes-Cahn-Hilliard system: Primitive Variable and Projection-Type Schemes
arXiv:1703.06606 · doi:10.1016/j.cma.2017.08.011
Abstract
In this paper we describe two fully mass conservative, energy stable, finite difference methods on a staggered grid for the quasi-incompressible Navier-Stokes-Cahn-Hilliard (q-NSCH) system governing a binary incompressible fluid flow with variable density and viscosity. Both methods, namely the primitive method (finite difference method in the primitive variable formulation) and the projection method (finite difference method in a projection-type formulation), are so designed that the mass of the binary fluid is preserved, and the energy of the system equations is always non-increasing in time at the fully discrete level. We also present an efficient, practical nonlinear multigrid method - comprised of a standard FAS method for the Cahn-Hilliard equation, and a method based on the Vanka-type smoothing strategy for the Navier-Stokes equation - for solving these equations. We test the scheme in the context of Capillary Waves, rising droplets and Rayleigh-Taylor instability. Quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes. Moreover, in all cases, mass of the single component and the binary fluid was conserved up to 10 to -8 and energy decreases in time.
References in corpus (4)
- A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation
- A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects
- A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law
- Diffuse-Interface Two-Phase Flow Models with Different Densities: A New Quasi-Incompressible Form and a Linear Energy-Stable Method
Cited by in corpus (20)
- Arbitrarily High-order Linear Schemes for Gradient Flow Models
- Arbitrarily High-order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
- 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
- Second-order Decoupled Energy-stable Schemes for Cahn-Hilliard-Navier-Stokes equations
- Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes
- A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes
- A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes
- Assessment of an energy-based surface tension model for simulation of two-phase flows using second-order phase field methods
- A Second Order Fully-discrete Linear Energy Stable Scheme for a Binary Compressible Viscous Fluid Model
- A consistent and conservative volume distribution algorithm and its applications to multiphase flows using Phase-Field models
- An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model
- A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow
- A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow
- An energy stable finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density
- Phase Field Modeling and Numerical Algorithm for Two-Phase Dielectric Fluid Flows
- Arbitrarily High-order Unconditionally Energy Stable Schemes for Gradient Flow Models Using the Scalar Auxiliary Variable Approach
- Model of the dynamics of an interface between a smectic phase and an isotropic phase of different density
- A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios
- Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces
- Global Weak Solutions to a Cahn-Hilliard-Navier-Stokes System with Chemotaxis and Singular Potential