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 viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Three-Dimensional Front Tracking
SIAM Journal on Scientific Computing
SIAM Review
Journal of Computational Physics
The point-set method: front-tracking without connectivity
Journal of Computational Physics
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Journal of Computational Physics
A conservative level set method for two phase flow
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
A grid based particle method for moving interface problems
Journal of Computational Physics
A self-adaptive oriented particles Level-Set method for tracking interfaces
Journal of Computational Physics
A gradient-augmented level set method with an optimally local, coherent advection scheme
Journal of Computational Physics
Hi-index | 31.45 |
In this work we present a new method for tracking evolving interfaces. Like the Adaptive Oriented Particle Level Set method (AOPLS, Ianniello and Mascio, 2010), it uses a combination of unconnected particles containing geometric information and a level set function to track the interface. In the present method, the geometric information, solved for in each particle, is a set of tangent vectors and the corresponding curvature tensor of the interface. Compared to the AOPLS method, the amount of geometric data stored in each particle is roughly halved, while still retaining a description of the interface that includes both orientation and curvature. A mechanism for ensuring a sufficiently dense distribution of particles on the interface is also included. From the information stored in each particle, a ''continuous'' representation of the interface is obtained by transferring the information to a level set function stored on an Eulerian grid. Unlike the AOPLS method, the present method takes the curvature into account when the zero level set is constructed. This results in significant improvements in regions of high curvature. Two different formulations of the new method have been explored. In the first, the tangent vectors deform purely according to the velocity field. In the second, the tangent vectors are forced to coincide with the principal directions of the surface. Both formulations are shown to be applicable.