I'm writing a relatively simple implementation of 2-D incompressible Navier-Stokes equations for MATLAB. The flow will be unsteady but laminar throughout.
A big irritation is an irregular domain. It would be very helpful if I could chop it up into a series of three or four rectangular domains. My question is, are there rules of thumb about whether this is acceptable from an accuracy perspective?
What I'd like to do is extrapolate the closest interior points to the boundaries at the "doorway" between successive sub-domains so that the output of one chamber is the input to another. I'm concerned that some sort of upstream effect will ruin my results. Any thoughts? I haven't been able to find any literature.
I haven't worked with MATLAB for CFD, but as far as extrapolation that you mention is concerned, its effect primarily lies on accuracy. A first order extrapolation (use the value as such) leads to formal first order accuracy, a linear extrapolation would lead to second order accuracy (on uniform grids) or atleast lesser errors on irregular grids. To begin with, for sake of validating your code, you could just start off with a first order extrapolation, as it is easier. There wouldn't be issues of "upstream effect ruining results" as long as you use upwinding, and use the right information. This is essentially what parallel unstructured solvers do; domain partitioning is the starting point when parallelising CFD solvers using MPI.
Hope this helps
Thanks very much for your reply.
I should have said "downstream effects" as I'm concerned that as the flow moves from left to right, the state of the right-most chamber will affect a middle chamber, etc. But I'm hoping that since a boundary condition on the left-most chamber is "driving" the flow, any downstream effects will be drowned out.
I think your thoughts still hold however. Again, thank you very kindly for your time.
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