1. Software for the Games Industry 9 November 2004 Fluid Gaming: Particle Methods for Fluid Mechanics and Visualisation Graham Wynn James Gray Richard West

2. 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?

3. 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

4. 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

5. 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

6. 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???? VpVp V r =-V p

7. 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

8. 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

9. 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?

10. 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

11. 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)