Moving towards Adaptive mesh refinement

In CFD, mesh plays a critical part in solving any problem. If I talk about the type of meshes, it could be many depending on the way you see it. Meshes can be uniform or non-uniform, structured or unstructured, rectangular or polyhedral etc. Be it any kind of mesh, its density is also very significant. By density, I mean the mesh size. How many grid points you are using to cover your physical domain? In problems where solution is smooth, comparatively fewer grid points could work well but in the areas where solution changes rapidly, such as shocks, turbulence, boundaries etc., a coarser grid can not capture it very nicely.  You need fine grids in such areas.

After solving unsteady flows using artificial compressibility method I am shifting my attention towards adaptive mesh refinement (AMR). Why? Because the moment I read the first paper by Marsha Berger about it, I felt positive and excited about it. The idea appeared very cool and very motivating to me. In AMR, we adaptively place fine meshes in the areas where finer meshes are required and coarser meshes in their required places. From adaptive, I mean that the mesh could change throughout the domain with time. This technique could save computational costs as compared to the case in which you are forced to use finer mesh in all the domain.

At this time, I have understood a little part of it. I am trying to get to know it better and write my codes. Below is my presentation from this week, you could get an idea about what I have understood so far.

AMR

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