Fluid Gaming: Particle Methods for Fluid Mechanics and Visualisation

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24 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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Software for the Games Industry


9 November 2004

Fluid Gaming
:


Particle Methods for Fluid
Mechanics and Visualisation

Graham Wynn

James Gray

Richard West

Software for the Games Industry


9 November 2004

Smooth Particle Hydrodynamics


Developed in late 70’s to model
Compressible Astrophysical fluid flows


Derivatives calculated without a grid


Good for tracking Free Surface Flows


Has been extended to Incompressible
Fluids and Solid
-
body applications


Calculates forces between particles


ONE MORE POINT?

Software for the Games Industry


9 November 2004

Smooth Particle Hydrodynamics

Kernel smoothes particles properties

Approximate functions by a
summation




Kernel
W(r
-
r
b
) is like a Gaussian

Use cubic
-
spline
-

only have to sum
over nearby particles

Derivatives are calculated by a similar
summation over kernel

Software for the Games Industry


9 November 2004

Kernel smoothes particles properties

Approximate functions by a
summation




Kernel
W(r
-
r
b
) is like a Gaussian

Use cubic spline so only have to sum
over neighbouring particles

Derivatives are calculated by a similar
summation over kernel

SPH Kernel Interpolation

Software for the Games Industry


9 November 2004

Advantages of SPH


Resolution (particles) are where the fluid is
so time isn’t wasted on empty grid cells


Handles free surface boundaries easily


Can calculate forces on objects in flow


Method can handle a variety of problems


Lack of grid means it can handle complex
flows without grid tangling

Software for the Games Industry


9 November 2004


Reflective Boundaries







Determine segment where
particle will intersect


Move particle to point of
intersection with segment


Reflect particle off boundary
with a perpendicular
velocity V
r
=
-
V
p



Boundaries


Traditionally boundaries
are rows of particles


Computationally intensive


Can be difficult to set up
complicated geometries


Reflect particles off
polygonal segments


Faster & uses less memory


Much easier to set up
complicated geometries


Similar to methods already
used in CGI Industry????


V
p

V
r
=
-
V
p

Software for the Games Industry


9 November 2004

Astronomy


Colliding Neutron stars


Mass 1.4 times of Sun


Diameter of London


Collide
-

Supernova


Produce heavy elements


Simulation


Compressible gas


Complex EOS


Self
-
gravity



Software for the Games Industry


9 November 2004

2D Incompressible Flow


Breaking water dam


Complex boundary
geometry


Handles breaks in surface


Simulation


Quasi
-
Incompressible EOS




Large
C
s


means large
pressure variations result in
small density fluctuations

Software for the Games Industry


9 November 2004

3D Incompressible Flow


3D Breaking dam


V
-
shaped barrier


Flow contained in a
rectangular box


Simulation


Same method as 2D


N log N scaling


Half million particles


ONE MORE POINT?


OR MAYBE TWO?

Software for the Games Industry


9 November 2004

Solid Body Dynamics


Ductile extension


Central necking and
fracture of beam


Simulation


Modify pressure term



Stresses
-

Hooke’s law



Complex deformations

Software for the Games Industry


9 November 2004

Summary/Future Directions


Modelling of fluid like systems


Real Time Applications


Simplify method to make it quicker


Particle visualisation techniques


Extend to model explosions


Extend to model Multi
-
phase flows (e.g.
water/foam)