A hybrid numerical method for three-dimensional spatially-developing free-shear flows
Journal of Computational Physics
A continuum method for modeling surface tension
Journal of Computational Physics
The dynamics of nucleation for the Cahn-Hilliard equation
SIAM Journal on Applied Mathematics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Sharp interface tracking using the phase-field equation
Journal of Computational Physics
New finite-element/finite-volume level set formulation for modelling two-phase incompressible flows
Journal of Computational Physics
Short note: Spontaneous shrinkage of drops and mass conservation in phase-field simulations
Journal of Computational Physics
Journal of Computational Physics
A nonstiff, adaptive mesh refinement-based method for the Cahn-Hilliard equation
Journal of Computational Physics
Diffuse interface model for incompressible two-phase flows with large density ratios
Journal of Computational Physics
International Journal of Computational Fluid Dynamics
Journal of Computational Physics
Adaptive pseudospectral solution of a diffuse interface model
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Coupled flow-polymer dynamics via statistical field theory: Modeling and computation
Journal of Computational Physics
3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids
Journal of Computational Physics
Three-dimensional, fully adaptive simulations of phase-field fluid models
Journal of Computational Physics
A conservative phase field method for solving incompressible two-phase flows
Journal of Computational Physics
A diffuse-interface method for two-phase flows with soluble surfactants
Journal of Computational Physics
Towards multi-phase flow simulations in the PDE framework Peano
Computational Mechanics
Journal of Computational Physics
Journal of Computational Physics
Computers & Mathematics with Applications
Numerical and computational efficiency of solvers for two-phase problems
Computers & Mathematics with Applications
Journal of Computational Physics
Numerical simulation of single droplet dynamics in three-phase flows using ISPH
Computers & Mathematics with Applications
Numerical simulation of the three-dimensional Rayleigh-Taylor instability
Computers & Mathematics with Applications
Time integration for diffuse interface models for two-phase flow
Journal of Computational Physics
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.55 |
Phase field models offer a systematic physical approach for investigating complex multiphase systems behaviors such as near-critical interfacial phenomena, phase separation under shear, and microstructure evolution during solidification. However, because interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations require resolution of very thin layers to capture the physics of the problems studied. This demands robust numerical methods that can efficiently achieve high resolution and accuracy, especially in three dimensions. We present here an accurate and efficient numerical method to solve the coupled Cahn-Hilliard/Navier-Stokes system, known as Model H, that constitutes a phase field model for density-matched binary fluids with variable mobility and viscosity. The numerical method is a time-split scheme that combines a novel semi-implicit discretization for the convective Cahn-Hilliard equation with an innovative application of high-resolution schemes employed for direct numerical simulations of turbulence. This new semi-implicit discretization is simple but effective since it removes the stability constraint due to the nonlinearity of the Cahn-Hilliard equation at the same cost as that of an explicit scheme. It is derived from a discretization used for diffusive problems that we further enhance to efficiently solve flow problems with variable mobility and viscosity. Moreover, we solve the Navier-Stokes equations with a robust time-discretization of the projection method that guarantees better stability properties than those for Crank-Nicolson-based projection methods. For channel geometries, the method uses a spectral discretization in the streamwise and spanwise directions and a combination of spectral and high order compact finite difference discretizations in the wall normal direction. The capabilities of the method are demonstrated with several examples including phase separation with, and without, shear in two and three dimensions. The method effectively resolves interfacial layers of as few as three mesh points. The numerical examples show agreement with analytical solutions and scaling laws, where available, and the 3D simulations, in the presence of shear, reveal rich and complex structures, including strings.