High-Resolution Flux-Based Level Set Method

Authors:
Peter Frolkovicˇ;Karol Mikula
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2007

Citing 0
Cited 3

A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach

SIAM Journal on Scientific Computing
Simulating free surface flow with very large time steps

EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Simulating free surface flow with very large time steps

Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation

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Abstract

A new high-resolution flux-based finite volume method for general advection equations in nondivergent form including a level set equation for moving interfaces is introduced. The method is applicable to the case of nondivergence free velocity and to general unstructured grids in higher dimensions. We show that the method is consistent and that the numerical solution fulfills the discrete minimum/maximum principle. Numerical experiments show its second order accuracy for smooth solutions as well as for solutions with discontinuous derivatives and on general unstructured meshes. Numerical examples for passive transport and shrinking of dynamic interfaces, including examples with topological changes, are presented using locally adapted two-dimensional and three-dimensional grids.