I've developed a small program to simulate incompressible bidimentional flows using finite differences.
I've read that refine mesh near boundaries gives better results but I don't know how to implement this technique.
The basic idea is to have the finest mesh near the boundary and increment it. To do this, I think that I need to define a function. But how and what else I need to define?
Hope that my question was clear so if you have any good course, paper, link or whatever else on the subject, thank you in advance.
Re: Mesh refinement
If you are dealling with Cartesian meshes (which assumably you must be since using finite differences), the usual rule is to apply an expoential growth of 1.1 to 1.4.
first cell height = h second cell height = h * 1.1 nth cell height = h * 1.1^(n-1)
In very old CFD books you see they use functions, to find either the cell height or position. But this doesn't seem to be the current vogue in grid generation.
ps (ignoring turbulent flow simulations) you want to refine your grid close to your boundary because as you want the change in "properties" across a cell to remain reasonably constant in magnitude.
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