WHAT IS A MODEL?

In recent years, modeling has been embraced by the materials processing community as a tool for understanding and improving manufacturing processes. Models are often implemented in computer programs, but there are important differences between a model and the computer code that implements it. A model is a set of equations used to represent a physical process. Finite element or finite difference methods, and the computer programs that implement them, are techniques to solve the equations of the model, but they are not the model itself. Our main emphasis will be on creating models – on reducing a physical process to a set of equations – especially models whose solution accurately describes the behavior of the process. Occasionally we also will explore numerical solution methods, often to point out where unenlightened use can lead you astray.

Whenever we create a model, we make assumptions about what phenomena are important to the behavior of the physical process. This is both good and bad. Assumptions help define the mathematical model and make it amenable to analysis. However, incorrect assumptions and erroneous information become part of the model and may well distort the results. Sometimes assumptions greatly simplify the model and permit an easy solution, but they may also cause important physical phenomena to be misrepresented or overlooked. Limiting the number of assumptions helps to avoid this problem but may make the model overly complex. Then the solution becomes difficult, and important information may be obscured.