For most people, CFD is about continuity and Navier-Stokes equations. But this is not always true.
One of the alternatives for CFD simulation is the lattice Boltzmann equation (LBE), where the fluid is treated as fictitious mesoscopic particles (not molecules). If you need something to make you sleepy, please read the short (and concise, and free) book: A Practical Introduction to the Lattice Boltzmann Method.
But for commercial CFD code, most are based on Navier-Stokes equations, and differ in the numerical method: finite volume, or finite element, or a hybrid of both. Finite difference based CFD is hard to find in commercial codes.
When Exa hit the market with the first commercial LBE based CFD code, PowerFlow, about 15 years ago, not so much buzz was created in CFD market. Actually, the first a few releases got not-so-good reviews, partially due to the marketing and sales issues (over-promising). Of course, apparently, in recent years, they got a lot of improvements in both solver and marketing. They also got a few big customers in the automotive industry. But it is still not considered as the mainstream CFD software among CFD practitioners. In the academic circle, there have … Read the rest “Navier-Stokes vs lattice Boltzmann: will it change the landscape of CFD?”