[MITgcm-devel] (not so) funny things happen in seaice_lsr and pickups

[Martin Losch]

The question marathon continues ...
Jinlun, my observation is, that the metric terms cause all the trouble  
(no problems so far in cubed sphere integration of any resolution, nor  
on cartesian grid).  I have the suspicion that the symmetry of the  
laplacian operator is broken, because the metric terms are distributed  
unevenly between left and right hand side of the u and v equations. In  
order to ensure the diagonal dominance of the coefficient matrix,  
would it be possible to move all metric terms to the rhs? Just  
wondering ...

BTW, the system seems to be stable when I have a non-zero ZMIN.

Martin

On Mar 9, 2009, at 5:54 PM, Jinlun Zhang wrote:

> Hi Martin,
>
> As you said, for B-grid, the value does not matter because of the  
> non-slip bc's. I am not sure about C-grid non-slip bc's. If you need  
> that value at the boundary for C-grid, it seems that your approach  
> probably makes better sense.
>
> Jinlun
>
> Martin Losch wrote:
>> Hi again,
>>
>> I have another question for Jinlun. I am now quite confident, that  
>> I have found all (serious) problems in the metric terms. However,  
>> my code still blows up. Could the discretization of \eta be a  
>> problem? On Z-points ("bottom left" corner of C-grid cell, on a B- 
>> grid this is where the velocities are), I average eta like this:
>>        DO j=1,sNy+1
>>         DO i=1,sNx+1
>>          etaMeanZ (I,J,bi,bj) =
>>     &         (           ETA (I,J  ,bi,bj)  + ETA (I-1,J  ,bi,bj)
>>     &         +           ETA (I,J-1,bi,bj)  + ETA (I-1,J-1,bi,bj) )
>>     &         / MAX(1.D0,maskC(I,J,  k,bi,bj)+maskC(I-1,J,  k,bi,bj)
>>     &         +          maskC(I,J-1,k,bi,bj) 
>> +maskC(I-1,J-1,k,bi,bj) )
>>         ENDDO
>>        ENDDO
>> In the B-grid code I find this:
>>        DO j=1-Oly+1,sNy+Oly
>>         DO i=1-Olx+1,sNx+Olx
>>          ETAMEAN(I,J,bi,bj) =QUART*(
>>     &          ETA(I,J-1,bi,bj) + ETA(I-1,J-1,bi,bj)
>>     &         +ETA(I,J  ,bi,bj) + ETA(I-1,J  ,bi,bj))
>>          ZETAMEAN(I,J,bi,bj)=QUART*(
>>     &          ZETA(I,J-1,bi,bj) + ZETA(I-1,J-1,bi,bj)
>>     &         +ZETA(I,J  ,bi,bj) + ZETA(I-1,J  ,bi,bj))
>>         ENDDO
>>        ENDDO
>> This means that \eta/\zeta on the boundaries are only half as large  
>> as in my C-grid discretization (however, these values may actually  
>> never be used because of the no-slip BCs on the B-grid). So I am  
>> wondering, what the "correct" value of \eta on the boundary is. I  
>> observe, that code with
>>        DO j=1,sNy+1
>>         DO i=1,sNx+1
>>          etaMeanZ (I,J,bi,bj) = 0.25 _d 0 *
>>     &         (           ETA (I,J  ,bi,bj)  + ETA (I-1,J  ,bi,bj)
>>     &         +           ETA (I,J-1,bi,bj)  + ETA (I-1,J-1,bi,bj) )
>>         ENDDO
>>        ENDDO
>> tends to be stable (at least in the shorter test that I made).  
>> Jinlun, what's your opinion on this?
>>
>> Martin