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This should then match the equations given in Jiang and Peng (1999).
| / (WENO_SMALL + SQ(f.p - 2.0 * f.c + f.m)); | ||
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| deriv = (-f.m + 3. * f.c - 3. * f.p + f.pp); | ||
| deriv = -(-f.m + 3. * f.c - 3. * f.p + f.pp); |
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This doesn't look right to me. In the limit of smooth f, r->1, so w->1/3. Then the left stencil gives 1./6.*f.mm - f.m + 1./2.*f.c + 1./3.*f.p, which is a 3rd order first derivative (see http://web.media.mit.edu/~crtaylor/calculator.html with points at -2,-1,0,1). Before this change the right stencil is similar, but after it the right stencil would give -2./3.*f.m + 1./2.*f.c + 1./6.*f.pp, which isn't a 3rd order first derivative. Maybe there was a typo in the paper you cited @d7919?
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Yes that's definitely possible.
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(in the other limit both branches reduce to a second order central difference, I'm a bit surprised it's second order rather than first order and one sided but that's without thinking about it too hard)
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Closing following input from @johnomotani combined with fix to MMS test in #1528 which suggests we do get 3rd order without the change proposed here. |
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This should then match the equations given in Jiang and Peng (1999).