I'd like to create a very rough animation of a wave crashing on a beach. I'm guessing it would have to be a particle simulator, where you code in the forces between the particles and then integrate forward in time. I've done similar things, like simulations of charged particles, but there the forces are pretty straightforward, whereas here I guess I'd have to account for 1) tides 2) gravity 3) water surface tension. These seem like widely different forces acting on different scales. I don't even know where to begin. Any hints or links to papers related to this topic?
This is, no doubt, one of the biggest challenges for realistic simulations: waves crashing, hair moving under wind and whatever other movement involving turbulence will be hard to solve.
Though it is true that one can solve the equations of motion for each individual particle in a 'molecular dynamics' fashion, that is just infeasible for a system that goes beyond a few million particles. What can be done instead is to solve the equations of motion for the fluid by coarse graining the whole liquid as a homogeneous material (solving Navier-Stokes equations) but, again, if the simulation involves turbulence the equations become very time consuming.
The big question is how accurate you need your results to be: if the idea is to make it look pretty and somewhat real there are a couple of models - mainly for graphical processors (gpu) - that can be used to simulate waves. There is a really nice (and recent) overview on the subject at Science called "Computation Physics in Film". I think it will answer most of your remaining questions.