Fluid simulation
Marek Trtík
PA199

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Motivation
Other pictures source: [5]

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uEuler approach:
uFluid is modelled by a vector field, representing the velocity of the fluid.
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uLagrange approach:
uFluid is modelled by set of particles.
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uSmoothed Particle Hydrodynamics:
uFluid is modelled by set of particles moved via a velocity vector field.
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uHight-field surface approximation:
uSuitable for simulation of only fluid’s surface, e.g., lake or ocean surface.
Outline

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Euler approach

Start: 0h05m ~15m

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Fluid Model


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Navier-Stokes Equations
advection
pressure
diffusion
external
accel.

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Gradient, Divergence and Laplacian


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Gradient, Divergence and Laplacian


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Adding Custom Quantities


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Boundary Conditions


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Discretize fields
2D grid

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Discretize derivatives


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Solving Equations


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Solving Equations


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Solving Equations


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Solving Equations


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Euler approach
DEMO!
https://paveldogreat.github.io/WebGL-Fluid-Simulation/
http://haxiomic.github.io/projects/webgl-fluid-and-particles/

Start: 0h28m ~2m

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Lagrange approach

Start: 0h30m ~10m

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Particles Simulation


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External Forces


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Lagrange approach
DEMO!

Start: 1h13m

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Smoothed Particle Hydrodynamics

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Smoothed Particle Hydrodynamics

Start: 1h05m ~8m

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Smoothed Particle Hydrodynamics


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Smoothed Particle Hydrodynamics


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Height-field surface approximation

Start: 1h15m ~7m

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Fluid Surface Model


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Discretize Model


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Hight-field surface approximation
DEMO!

Start: 1h22m

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u[1] W.J. Laan, S. Green, M. Sainz; Screen Space Fluid Rendering with Curvature Flow; I3D 2009.
u[2] S. Green; Screen Space Fluid Rendering for Games; GDC 2010.
u[3] Jos Stam; Stable Fluids; ACM Transactions on Graphics, 2001.
u[4] R.Bridson, M.Müller; Fluid simulation; SIGGRAPH 2007 course notes.
u[5] GPU Gems 3; Chapter 30: Real-Time Simulation and Rendering of 3D Fluids.
u[6] GPU Gems; Chapter 38: Fast Fluid Dynamics Simulation on the GPU;
https://developer.download.nvidia.com/books/HTML/gpugems/gpugems_ch38.html
u[7] C. Johanson; Real-time water rendering; Master thesis, Lund University,2004.
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References

Start: 1h24m