Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A front-tracking method for multiphase free boundary problems
SIAM Journal on Numerical Analysis
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
Tree methods for moving interfaces
Journal of Computational Physics
A new Eulerian method for the computation of propagating short acoustic and electromagnetic pulses
Journal of Computational Physics
A fixed grid method for capturing the motion of self-intersecting wavefronts and related PDEs
Journal of Computational Physics
Robust Computational Algorithms for Dynamic Interface Tracking in Three Dimensions
SIAM Journal on Scientific Computing
Interfacial dynamics for Stokes flow
Journal of Computational Physics
Boundary integral methods for multicomponent fluids and multiphase materials
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
An Introduction to Eulerian Geometrical Optics (1992–2002)
Journal of Scientific Computing
A level set based Eulerian method for paraxial multivalued traveltimes
Journal of Computational Physics
Accurate representation of surface tension using the level contour reconstruction method
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
A grid based particle method for evolution of open curves and surfaces
Journal of Computational Physics
Fast and robust tracking of fluid surfaces
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A hybrid level set-volume constraint method for incompressible two-phase flow
Journal of Computational Physics
Journal of Scientific Computing
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
An oriented particle level set method based on surface coordinates
Journal of Computational Physics
Hi-index | 31.47 |
We propose a novel algorithm for modeling interface motions. The interface is represented and is tracked using quasi-uniform meshless particles. These particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface. The underlying grid provides an Eulerian reference and local sampling rate for particles on the interface. It also renders neighborhood information among the meshless particles for local reconstruction of the interface. The resulting algorithm, which is based on Lagrangian tracking using meshless particles with Eulerian reference grid, can naturally handle/control topological changes. Moreover, adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad/oct-tree data structure. Extensive numerical examples are presented to demonstrate the capability of our new algorithm.