Paper Info
Title
Restoring the missing vorticity in advection-projection fluid solvers
Abstract
Most visual effects fluid solvers use a time-splitting approach where velocity is first advected in the flow, then projected to be incompressible with pressure. Even if a highly accurate advection scheme is used, the self-advection step typically transfers some kinetic energy from divergence-free modes into divergent modes, which are then projected out by pressure, losing energy noticeably for large time steps. Instead of taking smaller time steps or using significantly more complex time integration, we propose a new scheme called IVOCK (Integrated Vorticity of Convective Kinematics) which cheaply captures much of what is lost in self-advection by identifying it as a violation of the vorticity equation. We measure vorticity on the grid before and after advection, taking into account vortex stretching, and use a cheap multigrid V-cycle approximation to a vector potential whose curl will correct the vorticity error. IVOCK works independently of the advection scheme (we present examples with various semi-Lagrangian methods and FLIP), works independently of how boundary conditions are applied (it just corrects error in advection, leaving pressure etc. to take care of boundaries and other forces), and other solver parameters (we provide smoke, fire, and water examples). For 10 ~ 25% extra computation time per step much larger steps can be used, while producing detailed vorticial structures and convincing turbulence that are lost without correction.
Year
DOI
Venue
2015
10.1145/2766982
ACM Transactions on Graphics
Keywords
Field
DocType
fluid simulation,vorticity,advection
Mathematical optimization,Convection,Vorticity,Turbulence,Vortex stretching,Vorticity equation,Advection,Potential vorticity,Multigrid method,Mathematics
Journal
Volume
Issue
ISSN
34
4
0730-0301
Citations 
PageRank 
References 
16
0.70
24
Authors
3
Name
Order
Citations
PageRank
Xinxin Zhang1291.56
ROBERT BRIDSON254627.92
CHEN GREIF332143.63