Is there a simulation method that is not Monte Carlo? All simulation methods involve substituting random numbers into the function to find a range of values for the function. So are all simulation methods in essence Monte Carlo methods?
There are simulations that are not Monte Carlo. Basically, all Monte Carlo methods use the (weak) law of large numbers: The mean converges to its expectation. 

Then there are Quasi Monte Carlo methods. These are simulated with a compromise of random numbers and equally spaced grids to yield faster convergece.

Simulations that are not Monte Carlo are e.g. used in computational fluid dynamics. It is easy to model fluid dynamics on a "micro scale" of single portions of the fluid. These portions have an initial speed,  pressure and size and are affected by forces from the neighbouring portions or by solid bodies. Simulations compute the whole behaviour of the fluid by calculating all the portions and their interaction. Doing this efficiently makes this a science. No random numbers are needed there.

In meteorology or climate research, things are done similarly. But now, the initial values are not exactly known: You only have the meteorological data at some points where they have been measured. A lot of data has to be guessed. 

As these complicated problems are often not continuous in their input data, you run the simulations with different guesses. The final result will be chosen among the most frequent outcomes. This is actually how some weather forecasts are simulated in principle.
