Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
A numerical method for solving incompressible flow problems with a surface of discontinuity
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
An adaptive mesh algorithm for evolving surfaces: simulation of drop breakup and coalescence
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
Boundary integral methods for multicomponent fluids and multiphase materials
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Remeshed smoothed particle hydrodynamics simulation of the mechanical behavior of human organs
Technology and Health Care
A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant
Journal of Computational Physics
Journal of Computational Physics
A coupling interface method for elliptic interface problems
Journal of Computational Physics
A front-tracking method for computation of interfacial flows with soluble surfactants
Journal of Computational Physics
Redistancing by flow of time dependent eikonal equation
Journal of Computational Physics
An immersed boundary method for interfacial flows with insoluble surfactant
Journal of Computational Physics
Journal of Computational Physics
A conservative SPH method for surfactant dynamics
Journal of Computational Physics
A hybrid numerical method for interfacial fluid flow with soluble surfactant
Journal of Computational Physics
Phase-field modeling droplet dynamics with soluble surfactants
Journal of Computational Physics
A diffuse-interface method for two-phase flows with soluble surfactants
Journal of Computational Physics
Computational Modeling of Solid Tumor Growth: The Avascular Stage
SIAM Journal on Scientific Computing
Efficient numerical methods for multiple surfactant-coated bubbles in a two-dimensional stokes flow
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Computational Physics
A level-set continuum method for two-phase flows with insoluble surfactant
Journal of Computational Physics
A continuum model of interfacial surfactant transport for particle methods
Journal of Computational Physics
Connectivity-free front tracking method for multiphase flows with free surfaces
Journal of Computational Physics
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
Computers and Structures
An embedded boundary method for soluble surfactants with interface tracking for two-phase flows
Journal of Computational Physics
A level-set method for two-phase flows with moving contact line and insoluble surfactant
Journal of Computational Physics
Hi-index | 31.53 |
A level-set method for the simulation of fluid interfaces with insoluble surfactant is presented in two-dimensions. The method can be straightforwardly extended to three-dimensions and to soluble surfactants. The method couples a semi-implicit discretization for solving the surfactant transport equation recently developed by Xu and Zhao [J. Xu, H. Zhao. An Eulerian formulation for solving partial differential equations along a moving interface, J. Sci. Comput. 19 (2003) 573-594] with the immersed interface method originally developed by LeVeque and Li and [R. LeVeque, Z. Li. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994) 1019-1044] for solving the fluid flow equations and the Laplace-Young boundary conditions across the interfaces. Novel techniques are developed to accurately conserve component mass and surfactant mass during the evolution. Convergence of the method is demonstrated numerically. The method is applied to study the effects of surfactant on single drops, drop-drop interactions and interactions among multiple drops in Stokes flow under a steady applied shear. Due to Marangoni forces and to non-uniform Capillary forces, the presence of surfactant results in larger drop deformations and more complex drop-drop interactions compared to the analogous cases for clean drops. The effects of surfactant are found to be most significant in flows with multiple drops. To our knowledge, this is the first time that the level-set method has been used to simulate fluid interfaces with surfactant.