Download Simulation of Fluids using the Navier

Simulation of Fluids using the
Navier-Stokes Equations
Kartik Ramakrishnan
Presentation Scope
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Introduction
Theory
Adaptation to CPU and GPU
Results
Optimizations and Future Work
Introduction
• Physically based simulation of fluids produces
very good visual effects
• Computationally expensive process
• In the past,usually done offline and not in real
time
• Real time fluid simulation was done using
particle systems
• Current hardware makes physically based fluid
simulation possible in real time
Navier-Stokes Theory
• The fluid being rendered is assumed to be
incompressible (fluid volume remains constant
over time)
• The fluid being rendered is assumed to be
homogeneous (fluid density remains constant
in space)
Navier-Stokes Theory
RHS of the equation, proceeding left to
right,
•Advection/velocity term
•Pressure term
•Diffusion term
•Force term
Navier-Stokes Theory
• Advection
- Describes the transport mechanism of the
fluid
- Also describes the transport mechanism of
any material the fluid may be carrying
- For example , ink in water, the advection term
describes the movement of both the water
and the ink
Navier-Stokes Theory
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Diffusion
Describes the resistance of the fluid to flow
Viscosity of the fluid is a factor in this term
More viscous the fluid, the more resistant it is
to flow
- Impedes the velocity of the fluid
Navier-Stokes Theory
• Pressure
- Describes the behavior of the fluid due to
pressure induced among fluid particles
- Think fluid particles squished against each
other due to the application of force
- Pressure leads to increase in the velocity
Navier-Stokes Theory
• Force
- Describes the behavior the fluid due to any
externally applied force or any bodily force
(gravity)
- Application of force causes an increase in the
fluid velocity
Adaptation to CPU and GPU
• The NS equation is not in a finite form
• Need to reduce each of the above RHS terms
to a discrete representation that can be
implemented on the CPU and the GPU
Adaptation to CPU and GPU
• Finite representation of the NS Equation
Adaptation to CPU and GPU
• Discrete NS algorithm
- Assume a 2D bounding grid for the fluid
- Assume one such grid for each fluid property
of interest (velocity, pressure, force, dye etc.)
- Assume that velocity and pressure are 0 at
time t = 0
- Assume that velocity is negative and that
pressure is 0 at the grid boundaries
Adaptation to CPU and GPU
• Algorithm steps
- Apply force: w1 = u + Force* timestep
- Advect: w2 = w1(x – timestep*w1)
- Diffuse term: del2 w3 = w2
- Pressure term: del2 p = w3
- Subtract pressure gradient: w4 = w3 – del p
Adaptation to CPU and GPU
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void Fluids::Simulate()
{
//Advect
Advect(();
SwapVelocityGrid();
SwapColorGrid();
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//Add force
AddForce();
SwapVelocityGrid();
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//Diffuse
Diffuse();
SwapVelocityGrid();
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SetBounds();
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timestep++;
//Compute Pressure
ComputePressure();
SwapPressureGrid();
//Project
Project();
SwapVelocityGrid();
}
Results
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AMD Athalon 3200+ 2.19 GHz, 2GB RAM
AMD Radeon 4870 1GB
Brook+
64x64 fluid grid, 50 frames and 70 jacobian
iterations
• CPU (averaged over 50 frames) = 0.83 sec
• GPU (averaged over 50 frames) = 0.035 sec
Optimizations and Future Work
• Use float 4 for the pressure computation
instead of float
• Pinned memory, new to Brook+1.4
• Shared memory, supposed to be
implemented, but think its not
• GPU version still glitchy – needs a few tweaks
• Other fluid grid sizes
Distant future
• Better visuals
• Port to DirectX 10 : dedicated texture
hardware support available, bilinear
interpolation available for free
• Questions