Fluid simulation
Solving a fluid's motion in real time — on a grid or as a swarm of particles — and faking it wherever you can get away with it.
Two schools split the field. The Eulerian one solves the Navier–Stokes equations on a fixed grid; Jos Stam's Stable Fluids (1999) made that fast enough for interactive smoke and fire by trading physical accuracy for unconditional stability. The Lagrangian one tracks particles instead — SPH, smoothed-particle hydrodynamics — where each blob carries its own mass and velocity.
Either way, the surface is the hard part. An invisible field function has to become a visible surface, usually via marching cubes or a screen-space trick. So most games settle for pre-baked or faked fluid and save the real solver for the puddle you actually touch.