Numerical simulations are computer-based methods used to model and analyze complex systems by solving mathematical equations. They allow researchers to predict how systems behave under various conditions without needing to conduct physical experiments. This approach is widely used in fields like physics, engineering, and climate science. These simulations can represent anything from the flow of air over an airplane wing to the interactions of particles in a chemical reaction. By adjusting parameters in the simulation, scientists can explore different scenarios and gain insights that help improve designs, understand phenomena, or make informed decisions.