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
A fast level set method for propagating interfaces
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Review
Algorithm 611: Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
The constrained interpolation profile method for multiphase analysis
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
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
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 quadrature-free discontinuous Galerkin method for the level set equation
Journal of Computational Physics
Journal of Computational Physics
A study of numerical methods for the level set approach
Applied Numerical Mathematics
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
An accurate conservative level set/ghost fluid method for simulating turbulent atomization
Journal of Computational Physics
A spectrally refined interface approach for simulating multiphase flows
Journal of Computational Physics
A fast and accurate semi-Lagrangian particle level set method
Computers and Structures
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
An unconditionally stable fully conservative semi-Lagrangian method
Journal of Computational Physics
Hi-index | 31.45 |
We present and test a gradient augmented level set method for unstructured grids, which has been designed to allow for easy integration in parallel flow solvers. The means to this end is a Hermite formulation, where the gradient is stored and advected as an independent variable, along with the level set function. The method uses narrow-band storage in conjunction with a Fast Marching Method, which is also designed to take advantage of the gradient augmentation. We demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high-performing methods on structured grids.