An arbitrary Lagrangian-Eulerian computing method for all flow speeds
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Reconstructing volume tracking
Journal of Computational Physics
Tree methods for moving interfaces
Journal of Computational Physics
Journal of Computational Physics
A new volume of fluid advection algorithm: the stream scheme
Journal of Computational Physics
Journal of Computational Physics
Completely conservative and oscillationless semi-Lagrangian schemes for advection transportation
Journal of Computational Physics
Journal of Computational Physics
A volume of fluid method based on multidimensional advection and spline interface reconstruction
Journal of Computational Physics
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
Journal of Computational Physics
A hybrid particle-mesh method for viscous, incompressible, multiphase flows
Journal of Computational Physics
Coupling water and smoke to thin deformable and rigid shells
ACM SIGGRAPH 2005 Papers
A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods
Journal of Computational Physics
The repair paradigm: New algorithms and applications to compressible flow
Journal of Computational Physics
Efficient simulation of large bodies of water by coupling two and three dimensional techniques
ACM SIGGRAPH 2006 Papers
Advections with Significantly Reduced Dissipation and Diffusion
IEEE Transactions on Visualization and Computer Graphics
Computing a null divergence velocity field using smoothed particle hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A new interface tracking method: The polygonal area mapping method
Journal of Computational Physics
Two-Way Coupled SPH and Particle Level Set Fluid Simulation
IEEE Transactions on Visualization and Computer Graphics
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
Journal of Computational Physics
The fixed-mesh ALE approach for the numerical approximation of flows in moving domains
Journal of Computational Physics
A method for avoiding the acoustic time step restriction in compressible flow
Journal of Computational Physics
An Hamiltonian interface SPH formulation for multi-fluid and free surface flows
Journal of Computational Physics
A fast and accurate semi-Lagrangian particle level set method
Computers and Structures
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
FlowFixer: using BFECC for fluid simulation
NPH'05 Proceedings of the First Eurographics conference on Natural Phenomena
Mass and momentum conservation for fluid simulation
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A hybrid level set-volume constraint method for incompressible two-phase flow
Journal of Computational Physics
Simulating free surface flow with very large time steps
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Mass-conserving eulerian liquid simulation
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
Mass-conserving eulerian liquid simulation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A two-continua approach to Eulerian simulation of water spray
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
A hybrid Lagrangian-Eulerian formulation for bubble generation and dynamics
Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
Journal of Computational Physics
A gradient augmented level set method for unstructured grids
Journal of Computational Physics
Hi-index | 31.49 |
Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.