implementation of upwind scheme in MATLAB
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More of a CFD or numerical analysis question than a proper MATLAB question but I will try my luck.
I am trying to implement an upwind scheme in MATLAB, in order to solve a 1D compressible navier stokes equation, with a periodic boundary condition:
I am trying to perform the spatial diffrentiation using an upwind scheme, see the attahced file "upWindDiffv2". the scheme should be TVD or numericaly stable but it isn't, I get substantial numerical oscilations and the code diverges. see the attached file "main", it includes a "video" of the solution where the solution clearly diverges.
I am performing the temporal integration using eulers method. I tried other temporal integration methods and they did not work either. note that the CFL criterion is more than satisfied.
I am not sure what I am doing wrong. would be thankfull for any assistance.