Discrete formulation of differential equations   Next: Finite volume method Up: Simulating air flow Previous: Simulating air flow

#### Discrete formulation of differential equations

The first step in computer solutions of differential equations (such as the flow equation we are considering) is approximating continuous space with a set of discrete points. We then use this discrete set of points to approximate the real solution. In particular we would like to know the value of our function at each of the points so that we can derive the flow. The finer we make the points (closer together) the more accurate our simulations will be. For some simulations it is adequate to put the points on a regular grid such that the distance between points is constant over the whole grid. In other simulations it is important to get more accuracy in certain areas, in particular in areas where the function of interest is changing more rapidly. In such simulations one place more points in places of more interest.

The the data we are going to be using for this assignment (an airplane wing with flaps) has already been broken down into a set of points. This set of points is much denser in regions where airflow is likely to have more interesting effects, such as at the front of the wing and between the back of the wing and the flaps.

Guy Blelloch
Thu Jun 15 17:00:37 EDT 1995