Why should we do computer simulation?
We want to simulate waves and other dynamic systems on a computer because there are useful results produced by doing this:
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Aircraft and spacecraft design: air flow around wings and control surfaces, stability of flight performance especially for damaged aircraft.
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Special effects for films and videos
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King Kong (2005): scenes with Kong fighting dinosaurs in the vines, some of the ocean waves. All the dinosaurs' movements.
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Lord of the Rings: Gandalf and Bilbo's smoke rings and ship. Flying dragons. Gollum and other magical animals. Moria, Mordor, Ents and so on.
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Star Wars: laser sword fight on the lava river, mythical animals, explosions.
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Shrek pouring the milk into the glass.
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Perfect Storm: many of the ocean scenes.
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Most big films use some sort of simulations for special effects.
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Designing and testing road systems by simulating traffic flow. Computer networks are also simulated using similar techniques to simulate data traffic flow.
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Testing theories of global climate change, evolution of galaxies, stars, Saturn's rings, and many other scientific research problems.