In a new sponsored feature, part of Intel's Visual Computing site, Dr. Michael J. Gourlay of the University of Central Florida Interactive Entertainment Academy continues his multi-part series
that explains fluid dynamics and its simulation techniques.
In part two, Gourlay introduces two key concepts of fluid simulation: approximation -- practically speaking, the equations used are only approximations of reality -- and discretization -- the continuous mathematical model of fluids must necessarily be converted into a series of discrete values.
In this excerpt, the author gives an overview of discretization:
"When solving fluid dynamics equations numerically, you convert the original continuous problem (which has infinite degrees of freedom) into a discrete problem (which has finite degrees of freedom). The choice of discretization scheme influences other aspects of the simulation, including interpolation, approximating spatial derivatives, evolving in time, and satisfying boundary conditions.
"That discretization process has many forms -- too many to cover here -- so this article focuses on intuitive formulations: Discretize space, approximate spatial derivatives using that discretization, and rewrite the continuous equations by replacing spatial derivatives with those approximations.
The previous article presented Eulerian (fixed-coordinate) and Lagrangian (moving-coordinate) views of the fluid momentum and vorticity equations. Analogously, you can discretize space using grids, particles, or a hybrid of the two.
"Regardless of whether they use grid-based or mesh-free discretization, we give the name nodes to locations where the simulation explicitly represents values. "
The full five-page feature, which drills down into significantly more depth about the grid-based and mesh-free discretization methods, is now available to read on Gamasutra