Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Motion of multiple junctions: a level set approach
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
A variational level set approach to multiphase motion
Journal of Computational Physics
SIAM Journal on Scientific Computing
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Finite Difference WENO Schemes with Lax--Wendroff-Type Time Discretizations
SIAM Journal on Scientific Computing
On the Evolution of Vector Distance Functions of Closed Curves
International Journal of Computer Vision
Advections with Significantly Reduced Dissipation and Diffusion
IEEE Transactions on Visualization and Computer Graphics
A ghost-fluid method for large-eddy simulations of premixed combustion in complex geometries
Journal of Computational Physics
Derivative Particles for Simulating Detailed Movements of Fluids
IEEE Transactions on Visualization and Computer Graphics
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Simulation of bubbles in foam with the volume control method
ACM SIGGRAPH 2007 papers
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
Real-time fluid simulation using discrete sine/cosine transforms
Proceedings of the 2009 symposium on Interactive 3D graphics and games
A novel algorithm for incompressible flow using only a coarse grid projection
ACM SIGGRAPH 2010 papers
Practical animation of compressible flow for shock waves and related phenomena
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
An unconditionally stable fully conservative semi-Lagrangian method
Journal of Computational Physics
Mass and momentum conservation for fluid simulation
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A novel method for large crowd flow
Transactions on edutainment VI
Out-of-Core Computations of High-Resolution Level Sets by Means of Code Transformation
Journal of Scientific Computing
FlowFixer: using BFECC for fluid simulation
NPH'05 Proceedings of the First Eurographics conference on Natural Phenomena
Spatio-temporal extrapolation for fluid animation
ACM Transactions on Graphics (TOG)
Hi-index | 31.46 |
We propose a method that significantly improves the accuracy of the level set method and could be of value for numerical solutions of differential equations in general. Level set methods use a level set function, usually an approximate signed distance function, Φ to represent the interface as the zero set of Φ. When Φ is advanced to the next time level by an advection equation, its new zero level set will represent the new interface position. But the non-zero curvature of the interface will result in uneven gradients of the level set function which induces extra numerical error. Instead of attempting to reduce this error directly, we update the level set function Φ forward in time and then backward to get another copy of the level set function, say Φ1 ċ Φ1 and Φ should have been equal if there were no numerical error. Therefore Φ - Φ1 provides us the information of error induced by uneven gradients and this information can be used to compensate Φ before updating Φ forward again in time.