I am developing an algorithm generally applicable to CFD methods and I would like a professional opinion as to the relevance of my results so far. I am not seeking technical assistance with any sort of development, I would simply like to know if the work I have been doing is worth pursuing further.
As a test case I have a solution to Burgers equation with the initial conditions:
u = 5 + cos(2pi*x)
Calculated on a periodic grid no larger than N=40 and using an effective (maximum) Courant number of at least 9 up to just before the singularity my method produces errors on the order of 10^-5.
I think it is promising but I am not so well versed in CFD methods that I trust my own opinion to know how this compares to the plethora of methods already available. I would like to know if a method that produces this sort of stable result is worth pursuing or at least what standard i might judge my methods against (i.e. what a better test case would entail or what would qualify as an impressive achievement in CFL number or error).
you will probably have already read it, but migh i suggest the book Reiman solvers and numerical methods for cfd
the author is E.Toro.
you might find some decent comparison and testcases.
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