Journal of Computational Physics
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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 level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
The fast construction of extension velocities in level set methods
Journal of Computational Physics
SIAM Journal on Scientific Computing
Tree methods for moving interfaces
Journal of Computational Physics
Some Improvements of the Fast Marching Method
SIAM Journal on Scientific Computing
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
A level set projection model of lipid vesicles in general flows
Journal of Computational Physics
3DFLUX: A high-order fully three-dimensional flux integral solver for the scalar transport equation
Journal of Computational Physics
An oriented particle level set method based on surface coordinates
Journal of Computational Physics
A gradient augmented level set method for unstructured grids
Journal of Computational Physics
Hi-index | 31.47 |
The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient information, and evolves both quantities in a fully coupled fashion. This maintains the coherence between function values and derivatives, while exploiting the extra information carried by the derivatives. The method is of comparable quality to WENO schemes, but with optimally local stencils (performing updates in time by using information from only a single adjacent grid cell). In addition, structures smaller than the grid size can be located and tracked, and the extra derivative information can be employed to obtain simple and accurate approximations to the curvature. We analyze the accuracy and the stability of the new scheme, and perform benchmark tests.