Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Moving mesh methods based on moving mesh partial differential equations
Journal of Computational Physics
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
Journal of Computational Physics
Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows
Journal of Computational Physics
Approximation of Liquid Crystal Flows
SIAM Journal on Numerical Analysis
Journal of Computational Physics
An adaptive mesh algorithm for evolving surfaces: simulation of drop breakup and coalescence
Journal of Computational Physics
A level-set method for computing solutions to viscoelastic two-phase flow
Journal of Computational Physics
Journal of Computational Physics
Delaunay refinement mesh generation
Delaunay refinement mesh generation
Computation of multiphase systems with phase field models
Journal of Computational Physics
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
An arbitrary Lagrangian-Eulerian method for simulating bubble growth in polymer foaming
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
Journal of Computational Physics
Pressure boundary conditions for computing incompressible flows with SPH
Journal of Computational Physics
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Journal of Computational Physics
An arbitrary Lagrangian Eulerian method for three-phase flows with triple junction points
Journal of Computational Physics
Hi-index | 31.50 |
This paper describes a novel numerical algorithm for simulating interfacial dynamics of non-Newtonian fluids. The interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. The property and evolution of the interfacial layer is governed by a phase-field variable φ that obeys a Cahn-Hilliard type of convection-diffusion equation. This circumvents the task of directly tracking the interface, and produces the correct interfacial tension from the free energy stored in the mixing layer. Viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase-field framework. The greatest challenge of this approach is in resolving the sharp gradients at the interface. This is achieved by using an efficient adaptive meshing scheme governed by the phase-field variable. The finite-element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large-scale two-phase systems of complex fluids. In two-dimensional and axisymmetric three-dimensional implementations, the numerical toolkit is applied here to drop deformation in shear and elongational flows, rise of drops and retraction of drops and torii. Some of these solutions serve as validation of the method and illustrate its key features, while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces.