Most phenomena involved in physical systems are governed by well-defined scientific laws. These laws correlate different properties and provide insights to the states of a system and processes it undergoes. Mathematical models can therefore be derived based on the laws, allowing scientists and engineers to explain what has happened or predict what will happen.

If a mathematical model is too complicated to solve, a computer will be needed. Thus, we have a computational model that approximates the solution using some numerical algorithms. Computational models are now increasingly important parts of computer-aided design (CAD) packages, which are in the tool box of almost every engineer whose job involves research and development (R&D). Computational models are often called numerical simulations. So we will use the two terms interchangably.

Today's students need to have a fundamental understanding of what computational models are and how they can be used to accelerate R&D processes.

## A Modeling Example

The following is a simple model of solar heating of a house. Use the controls to play with it and explore how such a model contributes to developing an understanding of the physical variables and processes involved in designing solar houses.

Sunlight: Morning Noon Afternoon Night

Select
Rectangle
Ellipse
Polygon
Blob
Heating
Thermometer

Reload the entire page to reset the model and the buttons.

Coloring:

 Isotherm lines Heat flux lines Heat flux arrows Graph Grid Ruler Color palette See-through