Desingularization of periodic vortex sheet roll-up
Journal of Computational Physics
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
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
A continuum method for modeling surface tension
Journal of Computational Physics
An Eulerian approach for vortex motion using a level set regularization procedure
Journal of Computational Physics
Regularization of ill-posed problems via the level set approach
SIAM Journal on Applied Mathematics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
SIAM Journal on Scientific Computing
Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Boundary integral methods for multicomponent fluids and multiphase materials
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Journal of Computational Physics
Stretching and wiggling liquids
ACM SIGGRAPH Asia 2009 papers
Singularity formation in a model for the vortex sheet with surface tension
Mathematics and Computers in Simulation
SIAM Journal on Scientific Computing
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A Eulerian fixed grid approach to simulate the dynamics of two-phase interfaces in the presence of surface tension forces is presented. This level set/vortex sheet method consists of a simplified system of equations that contain individual source terms describing the relevant physical processes at the phase interface explicitly. Hence, this approach provides a framework that will allow for a simplified subsequent modeling of phase interface dynamics in turbulent environments. In the presented level set/vortex sheet method, the location and the motion of the phase interface are captured by a level set equation. Topological changes of the interface, like breakup or merging, are thus handled automatically. Assuming that all vorticity is concentrated at the phase interface, the phase interface itself constitutes a vortex sheet with varying vortex sheet strength. The Eulerian transport equation for the vortex sheet strength is derived by combining its Lagrangian formulation with the level set equation. The resulting differential equation then contains source terms accounting for the stretching of the interface and the influence of surface tension, thus allowing for a detailed study of each effect individually. The results of three test problems, namely the roll-up of a vortex sheet without surface tension, the growth of the Kelvin-Helmholtz instability in the linear regime, and the long-time evolution of the Kelvin-Helmholtz instability are presented.