Marker-and-cell method

The marker-and-cell method is like playing "connect the dots" with a bunch of little dots, except the dots are used to keep track of something or someone moving in a fluid (like water or air).

Imagine you are playing with a bunch of small colored balls in a pool full of water. You want to know how the water moves around the balls as you move them around. Instead of just watching the water, you use a marker-and-cell method.

You grab a special piece of paper that has a bunch of squares on it, kind of like a grid. Each square is big enough to fit one of your colored balls. You also grab a marker to draw lines on the paper.

Every time you move one of your balls, you put a little dot on the square where the ball is. Then you draw a line connecting all the dots. This helps you see how the water moves around the balls.

But what if the balls move really fast or you can't see them all the time? Well, you have a special rule that says every time a ball moves into a new square, it leaves a little "stamp" behind. This "stamp" helps you keep track of where the ball has been, even if it's not there anymore.

So, in the end, you have a bunch of little dots and lines all over your grid paper. These dots and lines show you the paths that the balls took and how the water moved around them. This helps you figure out things like how fast the water was moving, where it was going, and how it was changing over time.

That's basically what the marker-and-cell method does, but instead of balls in a pool, it's used to study things like air currents in a room or water flowing through pipes. The dots and lines are used to keep track of how the fluid is moving over time, helping scientists and engineers study and understand complex systems.