Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
A Level Set Approach for the Numerical Simulation of Dendritic Growth
Journal of Scientific Computing
Finite Elements in Analysis and Design
Journal of Computational Physics
Adaptive knot placement in B-spline curve approximation
Computer-Aided Design
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth
Journal of Scientific Computing
A Local Semi-Implicit Level-Set Method for Interface Motion
Journal of Scientific Computing
Journal of Computational Physics
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
Hi-index | 31.46 |
An advantage of using level set methods for moving boundary problems is that geometric quantities such as curvature can be readily calculated from the level set function. However, in topologically challenging cases (e.g., when two interfaces are in close contact), level set functions develop singularities that yield inaccurate curvatures when using traditional discretizations. In this note, we give an improved discretization of curvature for use near level set singularities. Where level set irregularities are detected, we use a local polynomial approximation of the interface to construct the level set function on a local subgrid, where we can accurately calculate the curvature using the standard 9-point discretization. We demonstrate that this new algorithm is capable of calculating the curvature accurately in a variety of situations where the traditional algorithm fails and provide numerical evidence that the method is second-order accurate. Examples are drawn from modified Hele-Shaw flows and a model of solid tumor growth.