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Transcript of Fluid Dynamics
1978 "The Compleat Angler" by Whitted 1982 "Carla's Island" by Nelson Max already used linear approx of Strokes Model
no refraction of light formation of self-replicant patterns, only deep water -> no breaking waves etc. until about 1986:
Research focus on bump mapping
actual surface is flat
no animated waves
like view from airplane 1986 Fournier and Reeves:
A simple model of ocean waves (Siggraph 86) Uses particle systems to model foam and spray
(waves breaking, surface collisions) CFD Computational Fluid Dynamics "Fluid Dynamics is the study of fluids in motion. The basic equations governing fluid motion have been known for more than 150 years and are called the Navier-Stokes equations which govern the motion of a viscous, heat conducting fluid." 1989-1992
melting / freezing
wetting / drying
flow of water
droplets and droplet streams
interaction with dynamic and static floating objects Simulation of Fluid Dynamics
Two main approaches:
simulated by interaction of large number of particles
described by a set of partial differential equations ot be solved
second approach is more realiable and realistic in terms of physics simulation Navier-Stokes eqs. a continuous, amorphous substance whose molecules move freely past one another and that has the tendency to assume the shape of its container; a liquid or gas
a state of matter, such as liquid or gas, in which the component particles (generally molecules) can move past one another. Fluids flow easily and conform to the shape of their containers 1988 K. Sims: Particle animation and rendering
using parallel computation (SIGGRAPH) Definition Stress definition measure of the internal forces acting within a deformable body
internal forces are a reaction to external forces applied on the body
internal forces are distributed continuously within the volume of the material body, and result in deformation of the body's shape 1990 Kass & Miller: Rapid, stable fluid dynamics for
computer graphics (SIGGRAPH) acceleration force Shear stress - normal stress F=ma 1996-1998: Nick Foster & Dimitris Metaxas:
Several groundbreaking papers, doing fluid dynamics
by solving the 3D Navier Strokes-Equations Problem: Eulerian solvers used have unstable behaviors
for large time steps -> limits to speed and interactivity shear stress arises from a force orthogonal to the surface normal
normal stress arises from a force parallel or antiparallel to the surface normal Navier-Stokes for Incompressible Flow of Newtonian Fluids 1999 J. Stam: Stable fluids (SIGGRAPH)
uses the same method, switches Eulerian Solvers for a combination of Lagraian and implicit methods,
extended 2001 to use fourier transformation ρ Viscosity definition = density 2000+
2001: Kunimatsu - Fast simulation and rendering techniques
2001: Premoze - Rendering Natural Waters (whitecap analysis)
2001: Foster & Fedkiw - Practical animation of liquids
2002: Sloan - global illumination effects for dynamic real-time lightning
2003: Osher & Fedkiw - Level Set Methods and dynamic implicit surfaces (smooth surface & water breakdown) v = speed p = pressure describes a fluid's internal resistance to flow
viscosity is the thickness or internal friction
water is "thin", having a lower viscosity
honey is "thick", having a higher viscosity
real fluids have some resistance to stress and therefore are viscous
so called ideal fluid has no resistance to shear stress = dynamic viscosity 2010 Wotjan: Physics Inspired Topology Changes
in thin liquid surfaces Newton's law of viscosity the applied force is proportional to the area and velocity of the plate and inversely proportional to the distance between the plates 2010 Commercial State of the Art:
Scanline Flowline (2011 Academy Award Nomine &
VES Winner for visual effects) Tsunami Scene: Hereafter 2010 Newton's law of viscosity constitutive equation (like Hooke's law, Ohm's law)
Newton's law of viscosity is a approximation that holds true for some materials and fails others
Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity Types of viscosity Newtonian: fluids, such as water and most gases which have a constant viscosity = nabla operator Types of viscosity Shear thickening: viscosity increases with the rate of shear
Example: Silly Putty Types of viscosity Shear thinning: viscosity decreases with the rate of shear
Example: ketchup partial derivations in 3 dimensional cartesian coordinate systems Types of viscosity Types of viscosity Rheopectic: materials which become more viscous over time when shaken, agitated, or otherwise stressed
Example: whipped cream Types of viscosity Bingham plastic behaves as a solid at low stresses but flows as a viscous fluid at high stresses
Example: margarine equations that have such partial derivations are called Partial Differential Equations References:
T. Witthed, An improved illumination model for shaded
display, Commun. ACM 23 (6) (1980) 343–349.
N.L. Max, Carla’s Island, Siggraph Video Rev. (5) (1981).
A. Fournier, W.T. Reeves, A simple model of ocean waves,
in: Proceedings of SIGGRAPH’86, Comput. Graph. 20 (4)
K. Sims, Particle dreams (Video), Segment 42, Siggraph
Video Rev. 38/39 (1988).
M. Kass, G. Miller, Rapid, stable fluid dynamics for computer
graphics, in: Proceedings of SIGGRAPH’90, Comput. Graph.
24 (4) (1990) 49–57
N. Foster, D. Metaxas, Realistic animation of liquids, in: Pro-
ceedings of Graphics Interface’96, Calgary, Canada, (1996),
pp. 204–212; N. Foster, D. Metaxas, Realistic animation of liq-
uids, Graph. Models Image Process. 58 (5) (1996) 471–483.
N. Foster, D. Metaxas, Modeling the motion of a hot, turbulent
gas, in: Proceedings of SIGGRAPH’97, 1997, pp. 181–188.
N. Foster, D. Metaxas, Controlling fluid animation, in: Pro-
ceedings of Computer Graphics International CGI’97, IEEE
Computer Society Press, Menlo Park, CA, 1997, pp. 178–188 Thixotropic: materials which become less viscous over time when shaken, agitated, or otherwise stressed
Example: Toothpaste "In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several independent variables and their partial derivatives with respect to those variables." J. Stam, A simple fluid solver based on FFT, J. Graph. Tools
6 (2) (2001) 43–52.
A. Kunimatsu, Y. Watanabe, H. Fujii, T. Saito, K. Hiwada, T.
Takahashi, H. Ueki, Fast simulation and rendering techniques
for fluid objects, in: Proceedings of EUROGRAPHICS’01,
Comput. Graph. Forum 20 (3) (2001) 57–66.
S. Premoze, M. Ashikhmin, Rendering natural waters, in:
Proceedings of Pacific Graphics’00, 2000, pp. 23–30; S.
Premoze, M. Ashikhmin, Rendering natural waters, Comput.
Graph. Forum 20 (4) (2001) 189–199.
N. Foster, R. Fedkiw, Practical animation of liquids, in:
Proceedings of SIGGRAPH’01, 2001, pp. 23–30.
P.P. Sloan, J. Kautz, J. Snyder, Precomputed radiance transfer
for real-time rendering in dynamic, low-frequency lighting
environments, in: Proceedings of SIGGRAPH’02, ACM
Trans. Graph. 21 (3) 2002 527–536.
S. Osher, R. Fedkiw, The Level Set Method and Dynamic
Implicit Surfaces, Springer-Verlag, New York, 2002.
Wojtan, C., Thürey, N., Gross, M. & Turk, G. Physics-inspired topology changes for thin fluid features. ACM Transactions on Graphics 29 (1) (2010). Simulation and Theory of Fluids Advanced Computer Graphics
Frieder Nake Daniel Beßler Philipp Steiner Uğur Mutlu let's say I have an ideal liquid...
then I can also use Euler Equations ...though, Euler cannot solve heat conduction that Navier Stokes can... Should be visually plausible
Physical accuracy not paramount
Animators/director want a certain visual style ...BUT... ...animators' demands are different than in CFD... Simulation speed – deadlines and interactive preview
The fluid should have character
The artists want control – it should be possible to sculpt the fluid so... in 5 minutes thanks for your interest...
any questions? the equation can be expressed in terms of shear stress