Basic fluids

F LUID S IMULATION Robert Bridson, UBC Matthias Müller-Fischer, AGEIA Inc.

Course Details ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Symbols ,[object Object],[object Object],[object Object],[object Object],[object Object]

The Equations ,[object Object],[object Object],[object Object]

The Momentum Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Forces on Fluids ,[object Object],[object Object],[object Object]

Pressure ,[object Object],[object Object],[object Object],[object Object],[object Object]

Viscosity ,[object Object],[object Object],[object Object]

The Continuum Limit (1) ,[object Object],[object Object],[object Object],[object Object]

The Continuum Limit (2) ,[object Object],[object Object],[object Object]

Lagrangian vs. Eulerian ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Material Derivative (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Material Derivative (2) ,[object Object],[object Object]

Turning Dq/Dt Around ,[object Object],[object Object],[object Object],[object Object]

Writing D/Dt Out ,[object Object]

D/Dt For Vector Fields ,[object Object],[object Object],[object Object],[object Object]

Du/Dt ,[object Object],[object Object]

The Incompressibility Condition

Compressibility ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Incompressibility ,[object Object],[object Object],[object Object]

Divergence ,[object Object],[object Object],[object Object]

Pressure ,[object Object],[object Object],[object Object],[object Object]

Alternative ,[object Object],[object Object],[object Object],[object Object]

Dropping Viscosity ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Aside: A Few Figures ,[object Object],[object Object],[object Object],[object Object],[object Object]

The inviscid equations ,[object Object]

Boundary Conditions ,[object Object],[object Object],[object Object],[object Object],[object Object]

Solid Wall Boundaries ,[object Object],[object Object],[object Object],[object Object]

Free Surface ,[object Object],[object Object],[object Object]

Multiple Fluids ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Splitting ,[object Object],[object Object],[object Object],[object Object],[object Object]

A Splitting Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Does it Work? ,[object Object]

Splitting Momentum ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Space ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

A Simple Grid ,[object Object],[object Object],[object Object],[object Object],[object Object]

A Simple Grid Disaster ,[object Object],[object Object],u x

Staggered Grids ,[object Object],[object Object],[object Object],[object Object]

The MAC Grid ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Array storage ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The downside ,[object Object],[object Object],[object Object],[object Object]

Advecting Quantities ,[object Object],[object Object],[object Object],[object Object],[object Object]

Semi-Lagrangian Advection ,[object Object],[object Object],[object Object],[object Object]

Finding x old ,[object Object],[object Object],[object Object],[object Object],[object Object]

Aside: ODE methods ,[object Object],[object Object],[object Object],[object Object],[object Object]

Details of x old ,[object Object],[object Object],[object Object]

Which u to Use? ,[object Object],[object Object],[object Object],[object Object]

Finding q(x old ) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Extrapolating u Into Solids ,[object Object],[object Object],[object Object]

Extrapolation ,[object Object],[object Object],[object Object],[object Object]

Integrating Body Forces ,[object Object],[object Object]

The Continuous Version ,[object Object]

The Poisson Problem ,[object Object],[object Object]

Discrete Pressure Update ,[object Object]

Discrete Divergence ,[object Object]

Discrete Boundaries ,[object Object],S S S E S S F S S E E F F F F F F F

What’s Active? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Example Solid Wall ,[object Object],[object Object],[object Object],[object Object],[object Object],S F

Discrete Pressure Equations ,[object Object],[object Object]

Simplified ,[object Object],[object Object],[object Object],[object Object],[object Object]

Linear Equations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Voxelization is Suboptimal ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Smoke As per [Fedkiw et al.’01]

Soot ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Heat ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Boussinesq and Buoyancy ,[object Object],[object Object],[object Object]

Open Boundaries ,[object Object],[object Object],[object Object],[object Object]

Where is the Water? ,[object Object],[object Object],[object Object],[object Object]

Marker Particles ,[object Object],[object Object],[object Object],[object Object]

Rendering Marker Particles ,[object Object],[object Object],[object Object],[object Object],[object Object]

Improvement ,[object Object],[object Object],[object Object],[object Object],[object Object]

Level Sets ,[object Object],[object Object],[object Object],[object Object]

Surface Capturing ,[object Object],[object Object],[object Object]

Reinitializing ,[object Object],[object Object],[object Object],[object Object],[object Object]

Computing Signed Distance ,[object Object],[object Object],[object Object]

Set Up ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Fast Sweeping ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Extrapolation ,[object Object],[object Object],[object Object]

Extrapolation (1) ,[object Object],[object Object],[object Object]

Extrapolation (2) ,[object Object],[object Object],[object Object],[object Object]

Basic fluids

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Basic fluids