At its engine plant in Texas, SpaceX is trying out a number of different injectors and other parameters to squeeze the most performance out of its engines, and it runs tests every day. These tests are expensive and, more importantly, even if you design engines and do physical testing on them and layer them with all manner of sensors on the outside, you cannot see what is going on inside the engines as they run. It is far better to simulate all of the components of the engine and their fuels and narrow down the injector configurations through simulations and then do the design, manufacturing, and physical testing on just a few, optimal configurations.
Lichtl says that people have tried to use wavelet compression before, and these particular simulations are based on work done by Jonathan Regele, a professor at the department of aerospace engineering at Iowa State University.
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