Computer simulation in science

Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description:

• a numerical simulation of differential equations that cannot be solved analytically, theories that involve continuous systems such as phenomena in physical cosmology, fluid dynamics (e.g. climate models, roadway noise models, roadway air dispersion models),continuum mechanics and chemical kinetics fall into this category.
• a stochastic simulation, typically used for discrete systems where events occur probabilistically, and which cannot be described directly with differential equations (this is a discrete simulation in the above sense). Phenomena in this category include genetic drift,biochemical or gene regulatory networks with small numbers of molecules. (see also: Monte Carlo method).

Specific examples of computer simulations follow:

• statistical simulations based upon an agglomeration of a large number of input profiles, such as the forecasting of equilibriumtemperature of receiving waters, allowing the gamut of meteorological data to be input for a specific locale. This technique was developed for thermal pollution forecasting .
• agent based simulation has been used effectively in ecology, where it is often called individual based modeling and has been used in situations for which individual variability in the agents cannot be neglected, such as population dynamics of salmon and trout (most purely mathematical models assume all trout behave identically).
• time stepped dynamic model. In hydrology there are several such hydrology transport models such as the SWMM and DSSAM Modelsdeveloped by the U.S. Environmental Protection Agency for river water quality forecasting.
• computer simulations have also been used to formally model theories of human cognition and performance, e.g. ACT-R
• computer simulation using molecular modeling for drug discovery
• computer simulation for studying the selective sensitivity of bonds by mechanochemistry during grinding of organic molecules.^[6]
• Computational fluid dynamics simulations are used to simulate the behaviour of flowing air, water and other fluids. There are one-, two- and three- dimensional models used. A one dimensional model might simulate the effects of water hammer in a pipe. A two-dimensional model might be used to simulate the drag forces on the cross-section of an aeroplane wing. A three-dimensional simulation might estimate the heating and cooling requirements of a large building.
• An understanding of statistical thermodynamic molecular theory is fundamental to the appreciation of molecular solutions. Development of the Potential Distribution Theorem (PDT) allows one to simplify this complex subject to down-to-earth presentations of molecular theory.

Notable, and sometimes controversial, computer simulations used in science include: Donella Meadows' World3 used in the Limits to Growth, James Lovelock's Daisyworld and Thomas Ray's Tierra.