## Math in Engineering## Basics of Engineering |

## How are modeling and simulation used in engineering? |

Modeling and simulation have become an essential part of engineering on both a small and large scale. Because building any sized structure takes time and money, engineers often develop a mathematical model, a set of equations that describe what may happen to a structure if it is built the way it is represented by the model. Using a computer (or graphic) representation gives the engineers a three-dimensional view.

For example, before the International Space Station was built, engineers used mathematical modeling to simulate what the entire station would eventually look like in three dimensions. In this way, the engineers learned how the ISS would orbit the Earth, how solar energy could be used to run the ISS, and even how to allow the various international spacecraft to dock with the station. The computer was the only way to solve such problems without real-life testing. It quickly and easily solved a plethora of mathematical equations, especially using such mathematics as calculus and differential equations.

Another more down-to-earth example is hydraulic modeling. Engineers need to know how the water will flow around and push on bridge pilings, how to control drainage in cities and along coastline, and even how water flows through a city’s culvert system. For example, the United States Geological Survey (USGS) often develops one-, two-, or three-dimensional computer models of bridges over certain major rivers. With such models they can understand such conditions as how the water surface elevations change (especially crucial for estuaries along the coast that are affected by the tides), the runoff from other creeks and drainage areas that flow into the river, and the velocity distribution of the river—for low and high flow events (flood conditions)—and how these conditions will affect the bridge. Such details can also help other engineers who deal with structures found around the river, such as dams, levees, and even how erosion and deposition of sediments affect the river’s floodplain.