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
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Simplified discretization of systems of hyperbolic conservation laws containing advection equations
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 fast and accurate semi-Lagrangian particle level set method
Computers and Structures
Journal of Computational Physics
Hi-index | 31.45 |
We present a new approach to perform Eulerian level set interface tracking. It consists in advecting the level set function using a second-order two-way wave equation instead of the standard one-way wave advection equation. The resulting numerical schemes are simple to implement, more stable, and significantly less prone to dissipation errors than popular (e.g., WENO) discretizations of the one-way advection equation of higher order, in particular for long advection times. While both the two-way wave advection and the associated numerical schemes were derived previously, these approaches have never been combined with level set advection. Since the level set function to advect is smooth by construction, this ensures the stability of the solution when using the two-way advection equation discretized using centered finite difference schemes. Our numerical tests show that the two-way wave equation approach yields more accurate results than the standard one-way wave equation for the level set advection, at a considerably smaller computational cost.