This document summarizes a technique called position based fluids. It describes how smoothed particle hydrodynamics (SPH) and position based dynamics (PBD) are used. SPH uses kernel functions to compute density from particle positions. PBD iteratively solves constraints to update positions implicitly. The technique uses a scalar density constraint based on target density. It also applies artificial pressure and vorticity confinement forces. It can simulate fluids with 128k particles at 16ms per frame using this position based approach.
5. Smoothed particle hydrodynamics
“Particle-Based Fluid Simulation for
Interactive Applications”
M. Muller, D. Charypar, M. Gross
Symposium on Computer Animation 2003
17. Traditional approaches to simulation
1. All forces are accumulated
2. Using the density, the forces are
transformed into accelerations
3. Compute velocities from the accelerations
and then positions from the velocities
21. Stability
“Position Based Dynamics”
M. Muller, B. Heideberger, M. Hennix, J. Ratcliff
Workshop in Virtual Reality Interactions and
PHYsical Simulation (VRIPHYS) 2006
24. Implicit / explicit
“The integration does not fall clearly into the
category of implicit or explicit schemes.”
1 iteration: explicit
More iteration: implicit
25. Advantages
“The scheme is unconditionally stable.”
Steps (13) and (14) do not extrapolate blindly into
the future as traditional explicit schemes do
