Gaseous Phenomena
© Copyright 2003-15, Howard J. Hamilton, University of Regina
Main Reference for this page: Computer Animation: Algorithms and
Techniques by Rick Parent (Section 8.2 in the second edition, Section
5.3 in the first edition)
Gaseous Phenomena
- difficult to model since gas has no fixed geometry
- usually treated as compressible as opposed to liquids which are not
- a steady state flow indicates constant velocity and acceleration
through space
- vortices are circular swirls like a tornado
1. General Approaches to Modeling Gas
- there are three main approaches used to model gas
A. grid-based methods (Eulerian formulations)
B. particle-based methods (Lagrangian formulations)
C. hybrid methods
A. Grid-Based Method
o break space into equal-sized cells and then calculate the flow of gas
among the individual cells
o mass in each cell is therefore updated at each time interval
o since all cells have equal size, density is directly proportional to
mass
o we can use the density to determine visibility and illumination during
rendering
o gas attributes (i.e., velocity, mass, etc) can be used to control
movement from cell to cell
Flow out: based on cell size and the mass and velocity of the gas in
the cell
Flow in: based on the movements of gas from the surrounding cells
o changes in a cell can occur when external forces (i.e., wind, object
movement, etc) go through a cell
o the animator must either define the cells before rendering (fixed
number throughout but
low overhead) or allocate and deallocate
cells throughout the procedure (flexible number but
high
overhead)
Example:
o We can simulate gases moving through 2D space by updating the
position of each cell-sized mass of gas independently at each time
step.
o The update is done by determining a new position based on the old
position plus the velocity.
o Suppose that the new position is represented by a shape of the same
size as the original cell.
o Since this may overlap several cells, we determine which cells, and
then distributed the mass from the original cell to these cells in
proportion to the extent the shape overlaps the cells.
o Recall that we assume that all cells have the same size.
o If two or more bodies of gas flow into the same cell, then their
masses are added and a new velocity is computed based on the
mass-weighted average of the inflowing gases (we compute a
weighted average to conserve momentum).
o Two tendencies:
o Since we combine inflowing gases whenever they are in the same
cell, the gas may become more concentrated with time;
o Since we divide outflowing gas whenever they straddle cell
boundaries, the gas may be more dispersed with time.
o Over time, in the example program, the latter tendency always
wins.
o For notes on how to program a gas simulation: see
http://www.cs.uregina.ca/~anima/Notes/Gas/GasSimulationProgram.htm
o For some classroom examples: see
o http://www.cs.uregina.ca/~anima/Notes/Gas/GasExample1.txt
output for first class example
o http://www.cs.uregina.ca/~anima/Notes/Gas/GasExample2.txt
output for second class example
o http://www.cs.uregina.ca/~anima/Notes/Gas/GasExample3.txt
output for third class example
o picture of real gases in space:
http://apod.nasa.gov/apod/ap080217.html
B. Particle-Based Method
o break the gas into particles or “globs” which flow through the
space (think particle systems)
o particles are given masses and external forces can act upon them
o
this method is similar to rigid body dynamics so the concepts
and equations are familiar
o
unfortunately, the number of particles needed to generate a
realistic animation is quite large
o so fewer, larger particles are used and they are typically
visualized as fuzzy images that combine well.
C. Hybrid Method
o break the space into cells and track the movement of particles
through those cells
2. Computational Fluid Dynamics (CFD)
- Physics-based methods of animating gas flow use computational fluid
dynamics (CFD)
- CFD is based on the Navier-Stokes (NS) equations, which are
differential equations that describe fluid flow.
 Gas flow can be modeled using the Navier-Stokes equations in
a grid-based format
 This approach uses the principles of conservation of
momentum, mass, energy
 The approach also takes into account the flow in and out of
cells
- Vortex-based methods (utilizing particle methods) can also be used.