Computational fluid dynamics
From its inception in the mid-1940s until the invention of cellular automaton fluids in the 1980s, essentially all computational fluid dynamics involved taking the continuum Navier-Stokes equations and then approximating these equations using some form of discrete mesh in space and time, and arguing that when the mesh becomes small enough, correct results would be obtained. Cellular automaton fluids start from a fundamentally discrete system which can be simulated precisely, and thus avoid the need for any such arguments. One issue however is that in the simplest cellular automaton fluids molecules are in effect counted in unary: each molecule is traced separately, rather than just being included as part of a total number that can be manipulated using standard arithmetic operations. A variety of tricks, however, maintain precision while in effect allowing a large number of molecules to be handled at the same time.