Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A conservative staggered-grid Chebyshev multidomain method for compressible flows
Journal of Computational Physics
Reconstructing volume tracking
Journal of Computational Physics
An analysis of the discontinuous Galerkin method for wave propagation problems
Journal of Computational Physics
The ghost fluid method for deflagration and detonation discontinuities
Journal of Computational Physics
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
An efficient implicit discontinuous spectral Galerkin method
Journal of Computational Physics
Some Improvements of the Fast Marching Method
SIAM Journal on Scientific Computing
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
A sharp interface method for incompressible two-phase flows
Journal of Computational Physics
Tracking discontinuities in hyperbolic conservation laws with spectral accuracy
Journal of Computational Physics
A spectrally refined interface approach for simulating multiphase flows
Journal of Computational Physics
Detail-preserving fully-Eulerian interface tracking framework
ACM SIGGRAPH Asia 2010 papers
A hybrid level set-volume constraint method for incompressible two-phase flow
Journal of Computational Physics
A new approach to sub-grid surface tension for LES of two-phase flows
Journal of Computational Physics
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Level set methodology is crucially pertinent to tracking moving singular surfaces or thin fronts with steep gradients in the numerical solutions of partial differential equations governing complex flow fields. This methodology must be consistent with the basic solution technique for the partial differential equations. To this end, a discontinuous spectral element approach is developed for level set advection and reinitialization as these methods are becoming increasingly popular for the solution of the fluid dynamic problems. Example computations are provided, which demonstrate the high order accuracy of the method.