Modifications to tracer advection mono #739
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@mark-petersen and @ambrad I've pulled together a draft PR to add thickness weighting to the high order fluxes. I've also included more commenting of 3rd/4th order fluxes to avoid confusion. I have not tested this beyond building it, but wanted to post for your comments. In particular can you verify my implementation of SG equation (11) with the full derivatives? I've included my derivation.
I will report back after testing. |
| (0.5_RKIND*hProv(k-1,iCell)*(hProv(k-1,iCell) + hProv(k,iCell))) | ||
| dzEdge = 0.5*(hProv(k-1,iCell) + hProv(k,iCell)) | ||
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| highOrderFlx(k, iCell) = w(k,iCell)*(0.5_RKIND*(tracerCur(k,iCell) + tracerCur(k-1,iCell)) - & |
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I think the primary spot where using hProv weighting will benefit the flux is in the 2nd-order part. Here, you've kept this as 1/2 (q(k) + q(k-1)) and used hProv only in the second-derivative estimates. The vertOrder2 code uses the hProv-weighted version based on a linear interpolant; I think you should bring this into this expression.
That aside, I think we should be cautious about making changes to this code without a vertical-direction convergence test.
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Thanks @ambrad you're right, I didn't even think about that. It is of course obvious that part is fixed grid too.
I also agree we should have a vertical advection convergence test. I started implementing that test with a postbac but didn't get it fully cleaned up.
adds non uniform grid weighting to 2nd order component of the high order vertical flux
| deriv2Km1 = (tracerCur(k-2,iCell) - tracerCur(k-1,iCell))/(0.5_RKIND*hProv(k-1,iCell)* & | ||
| (hProv(k-2,iCell) + hProv(k-1,iCell))) - (tracerCur(k-1,iCell) - tracerCur(k,iCell)) / & | ||
| (0.5_RKIND*hProv(k-1,iCell)*(hProv(k-1,iCell) + hProv(k,iCell))) | ||
| dzEdge = 0.5*(hProv(k-1,iCell) + hProv(k,iCell)) |
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0.5_RKIND rather than 0.5.
These formulas look fine, but again, it's best to verify them with a convergence test.
The arithmetic could be decreased a bit in the deriv2(m1)* and highOrderFlx lines with some algebra.
This PR does two things