Computational Fluid Dynamics - PowerPoint Presentation

Slide1

Computational Fluid Dynamicsin Real-Time

An

I

ntroduction

to

Simulation and Animation

of Liquids and Gases

Considered PapersReal-Time Fluid Dynamics for Games (2003)

by

Jos

Stam

previously worked on

Maya

; now with

NVidia

covers gases

Realistic Animation of Liquids (1996)

by

Nick Foster and

Dimitri

Metaxas

first attempt to solve

Navier

-Stokes in full 3-D

Practical

Animation of

Liquids (2001)

by Nick Foster and Ronald

Fedkiw

Particle-Based Fluid Simulation for Interactive Applications (2003)

by Matthias Mueller, David

Charypar

and Markus Gross

Real-Time AnimatedGas-Flow

R

endered using “density quads”

Grid-Based Water Animation

Hybrid Surface Model

Particle-Based Water AnimationParticles Point Splatting

Iso

-Surface

(Marching Cubes)

Difference between liquids and gasesGases have simpler free surfacesDensity

provides enough information for renderer

For liquids we must also produce a

smooth

enough

free surface at boundariesGases are compressibleDensity of liquids, generally, never changes

Gases

have often

negligible

viscosity

Liquids observe

more obvious friction at boundary interfaces

But both are guided by the same equations

Physics of Fluids: The Navier-Stokes Equations

Velocity field

:

Density distribution

:

u

= velocity,

ρ

= density,

κ

= rate of diffusion, S = source

influences

Conservation

of mass

:

∇ ⋅ u = 0i.e., at any point in time, all velocities added together, cancel each otherChange of pressure: Caused by movement of the liquid

Three componentsDiscretizationG

rid

P

articles

Algorithm

to solve the mathematical modelLinear solver\More about this next timeRendering

Billboarding

Particles

Point splatting

Iso

-surfaces

DiscretizationOld method: Propagate fluid state through a 2-D or 3-D grid

Every cell has

density

,

velocity

and pressure informationLiquid cells have 3 mutually exclusive states:

Full

Surface (boundary)

Empty

Object boundaries

must

coincide

with the grid

New method: Use

Smoothed-particle

hydrodynamics

Particles that allow for smooth interpolation between their positionsDefine rules for boundariesAt the system’s edgesFor interfaces with other objects or fluidsSources & Sinks

Grid-based algorithm for liquids (1996)

Define obstacles and initial configuration

Setup

grid

with initial configuration

Track surface in cellsSetup boundary conditions

Update

velocity

values

Update

pressure

values

Recalculate boundary information of surface cells

Update position

of surface and objects

Go to step 3

Rendering (2001): Hybrid Surface Model

Move mass-less

marker particles

through the grid

Use algorithm (e.g.

Marching Cubes) to determine a smooth iso-countourUse other particle information and isocountour to make local changes

There is more to renderingTransparencyReflection

Refraction

Soft shadows

FinThat’s it – For now!