Computational Fluid Dynamics in Computer Graphics - Page 3

Computational Fluid Dynamics

What is CFD?

CFD, to many practitioners in industry, should mean "Colorful Fluid Dynamics." The point here is that there is no magic to CFD: the results are only approximate solutions to the posed mathematical problem, subject to errors in problem description, algorithm accuracy and stability, and interpretation.

How do you do it?

You need to formulate the governing equations, and then solve them as best as possible. This is far easier said than done.

conservation of mass (simplest)
conservation of momentum (these first two are called the Navier-Stokes equations)
conservation of energy (for temperature variations)
numerous other relationships: perfect gas, baroclinic generation of vorticity, molecular diffusion, free surface effects, etc.
See more about the Navier-Stokes equations
See more fluid dynamics equations

Methods for solving fluids problems

There exist essentially three methods to solve these governing equations. Finite-difference schemes account for more than 95% of CFD done in non-CG industry, though it seems that particle methods are the most common in the CG industry.

Finite-difference - discretize the computational volume into cells, either external:

Or internal:

Then rewrite the governing equations, replacing derivatives with a spatially or temporally discretized form:

Then solve them either for a single stable solution, or march forward in time. These methods are often called Eulerian methods.
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Spectral - convert the governing equations to the frequency spectrum and solve them there
Particle - instead of tracking fluid values at fixed nodes or cells in the computational volume, allow particles to carry those values with them, these methods are often called Lagrangian methods.
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Mark J. Stock, Aerospace Engineering, The University of Michigan