[MITgcm-support] balancing the heat equation

[Allison Byrd]

Hello mitcgm-ers!!

I am trying to solve the heat equation
dVT/dt+uTx+vTy+wTz=KTxx+KTyy+KTzz
with the goal being the left and right hand side equaling each other  
to machine precision.  We have a large imbalance between the two sides  
and are lost to the small detail we are missing.

for the left hand side we use gTnm1 for dT/dt, and then take the  
forward difference of T to solve for uTx,vTy, and wTz.  For the right  
hand side we use Khorizontal=500 m2/sec. and Kvertical =  
KPPdiffKzT+2*10^-4m2/sec.  Perhaps we are misusing the KPP schemes?   
Has anyone ever done this before?? Any help would be greatly  
appreciated.

Allison Byrd
FSU Dept of Oceanography
Physical Oceanography
Office Room 403
byrd at ocean.fsu.edu

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