Unfortunately, the only example I know of is confidential, with a provisional patent filed. But what I can tell you is that we are already solving non-trivial problems some 3-6 orders of magnitude faster than FDM/FEM. Not quite navier-stokes tier, but still in the realm of PDEs.
Sorry I can't be more specific, such is the nature of cutting edge industry, as I'm sure you understand!
And not sure I see the point in patenting such a thing. If it's as good as you say, in less than six months a research group in some country where US patents aren't held in very high regard will have duplicated the work and either sell it as a service or publish it in the scientific literature. They might not even mention knowing about the patent at all! Things have been discovered by multiple people almost simultaneously so many times in the history of science that it's almost a natural law; it'd be impossible to prove foul play.
US patents can be used to prevent the sale or import of violating foreign products into the US market. It's still the largest market and US patents are still the lynchpin of any patent portfolio.
Simultaneous discovery does occur and primacy is difficult to prove. Most patent offices had first-to-file as the deciding rule, the USPTO adopted first-to-file a few years back to cut down on endless litigation.
I work in the field of numerical modelling (fluid simulation), and I haven't seen any convincing demos of anything but utterly trivial problems solved this way. Care to share some examples?
(There are some works that focus on fluid simulation for CGI. That's neat, but a) only interpolates between real simulation data, and b) doesn't achieve physical accuracy, just looks good.)