Adaptive mesh refinement

Adaptive mesh refinement is like a puzzle. Imagine you have a big puzzle and you want to solve it faster. Some parts of the puzzle are harder than others, like the ones with lots of little pieces. Instead of trying to solve the whole puzzle at once, you can break it up into smaller sections and focus on the harder parts first. This way, you can solve the puzzle faster and more efficiently.

In science and engineering, we also use puzzles, called numerical simulations, to study things like the weather, the behavior of fluids, or the movement of objects in space. It's a bit like solving a puzzle, but the pieces are numbers instead of shapes.

Adaptive mesh refinement helps us solve these puzzles faster by breaking up the simulation into smaller parts, just like in our puzzle example. But instead of using our eyes and hands, we use computers to divide the simulation into smaller pieces called cells or grids.

These cells can have different sizes depending on how complicated the simulation is in that particular area. Just like how some parts of a puzzle are harder, some parts of a simulation are more difficult to solve because there's more going on. The computer will make the cells smaller in those areas so it can focus on the hard parts first.

Once the computer solves the difficult parts, it can use that information to fill in the rest of the puzzle. This way, we can get more detailed and accurate results without using as much computer power and time.

Adaptive mesh refinement is like solving a puzzle in smaller, more manageable pieces so we can solve it faster and get better results. It's like having a super smart friend who can look at a puzzle and instantly know which parts to focus on first.