Upwind scheme

An upwind scheme is a way to figure out which way particles or things are moving, either left or right. Imagine you are running through a field with a gust of wind. If the wind is blowing from behind you, you would feel it on your back and continue running. But, if the wind is blowing from the front, you would feel it pushing against your face and slow down.

Now, let's say you have a bunch of particles moving in a certain direction, and you want to figure out where they will end up later. An upwind scheme works by figuring out which direction the "wind" is blowing based on the direction the particles are currently moving. If most of the particles are moving to the left, it means the "wind" is blowing from the left, and those particles will continue moving left. The upwind scheme measures how much of the particles are moving in which direction, and uses that to predict where they will go next.

It's like looking at a group of people walking down the street and guessing where they will end up based on which way most of them are walking. If everyone is walking to the left, you can assume they are headed in that direction. In the same way, an upwind scheme makes predictions based on where the majority of the particles are "walking." It's a really useful tool for understanding how things move and change over time.