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
A fast level set method for propagating interfaces
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Reconstructing volume tracking
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Review
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
A fast modular semi-Lagrangian method for moving interfaces
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A numerical method for two-phase flow consisting of separate compressible and incompressible regions
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Animation and rendering of complex water surfaces
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Directable photorealistic liquids
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
ACM SIGGRAPH 2005 Papers
Coupling water and smoke to thin deformable and rigid shells
ACM SIGGRAPH 2005 Papers
A semi-Lagrangian contouring method for fluid simulation
ACM Transactions on Graphics (TOG)
Hierarchical RLE level set: A compact and versatile deformable surface representation
ACM Transactions on Graphics (TOG)
A quadrature-free discontinuous Galerkin method for the level set equation
Journal of Computational Physics
Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets
Journal of Scientific Computing
Practical animation of turbulent splashing water
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Face offsetting: A unified approach for explicit moving interfaces
Journal of Computational Physics
Sharp interface tracking using the phase-field equation
Journal of Computational Physics
A study of numerical methods for the level set approach
Applied Numerical Mathematics
High-fidelity interface tracking in compressible flows: Unlimited anchored adaptive level set
Journal of Computational Physics
Derivative Particles for Simulating Detailed Movements of Fluids
IEEE Transactions on Visualization and Computer Graphics
Simulation of bubbles in foam with the volume control method
ACM SIGGRAPH 2007 papers
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Fast viscoelastic behavior with thin features
ACM SIGGRAPH 2008 papers
Technical Section: A simple and flexible framework to adapt dynamic meshes
Computers and Graphics
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
Front tracking with moving-least-squares surfaces
Journal of Computational Physics
Fast PDE approach to surface reconstruction from large cloud of points
Computer Vision and Image Understanding
Fast edge integration based active contours for color images
Computers and Electrical Engineering
An improved particle correction procedure for the particle level set method
Journal of Computational Physics
Fast and robust tracking of fluid surfaces
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Computer Aided Geometric Design
A self-adaptive oriented particles Level-Set method for tracking interfaces
Journal of Computational Physics
Vector fluid: a vector graphics depiction of surface flow
NPAR '10 Proceedings of the 8th International Symposium on Non-Photorealistic Animation and Rendering
Reconstructing surfaces of particle-based fluids using anisotropic kernels
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Extended papers from NPAR 2010: Vector graphics depicting marbling flow
Computers and Graphics
A Memory and Computation Efficient Sparse Level-Set Method
Journal of Scientific Computing
An unconditionally stable fully conservative semi-Lagrangian method
Journal of Computational Physics
A conservative level set method suitable for variable-order approximations and unstructured meshes
Journal of Computational Physics
A particle-based method for preserving fluid sheets
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Journal of Computational Physics
Liquid simulation with mesh-based surface tracking
ACM SIGGRAPH 2011 Courses
Journal of Computational Physics
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
Journal of Computational and Applied Mathematics
FlowFixer: using BFECC for fluid simulation
NPH'05 Proceedings of the First Eurographics conference on Natural Phenomena
A unified lagrangian approach to solid-fluid animation
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
Reconstructing surfaces of particle-based fluids using anisotropic kernels
ACM Transactions on Graphics (TOG)
Particle level set advection for the interactive visualization of unsteady 3D flow
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Highly adaptive liquid simulations on tetrahedral meshes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Chimera grids for water simulation
Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A hybrid Lagrangian-Eulerian formulation for bubble generation and dynamics
Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Hybrid particle---grid fluid animation with enhanced details
The Visual Computer: International Journal of Computer Graphics
A gradient augmented level set method for unstructured grids
Journal of Computational Physics
A level set two-way wave equation approach for Eulerian interface tracking
Journal of Computational Physics
A localized re-initialization equation for the conservative level set method
Journal of Computational Physics
Hi-index | 0.09 |
In this paper, we present an efficient semi-Lagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method with- out the adverse effects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD Runge-Kutta and HJ-WENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the level set method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semi-Lagrangian advection scheme coupled with a first order accurate fast marching method to evolve the level set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate method. Since we avoid complex high order accurate numerical methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octree-based adaptive mesh.