Bugs with adaptive vertical advection: 1) dynzdf.F90

[jchanut]

Context

Adaptive (based on courant number) vertical advection, ln_zad_Aimp=.true.

Analysis

There are a couple of bugs in dynzdf.F90 with ln_zad_Aimp=.true.
1) In building the tridiagonal matrix one uses the implicit vertical velocity at W-point:

zWui = 0.5_wp * ( wi(ji,jj,jk  ) + wi(ji+1,jj,jk  ) )
zWus = 0.5_wp * ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) )

which is multiplied later when filling the matrix by

zdt = r2dt * 0.5

which reads:

zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) 
zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp )
zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) )

It means that vertical velocities are multiplied by 0.5 twice instead of once.

2) Off diagonal terms should be divided by e3u, including implicit advection terms which is not the case.

Fix

U velocity case:

ze3ua =  ( 1._wp - r_vvl ) * e3u_n(ji,jj,jk) + r_vvl * e3u_a(ji,jj,jk)
...
zWui = ( wi(ji,jj,jk  ) + wi(ji+1,jj,jk  ) ) / ze3ua
zWus = ( wi(ji,jj,jk+1) + wi(ji+1,jj,jk+1) ) / ze3ua
zwi(ji,jj,jk) = zzwi + zdt * MIN( zWui, 0._wp ) 
zws(ji,jj,jk) = zzws - zdt * MAX( zWus, 0._wp )
zwd(ji,jj,jk) = 1._wp - zzwi - zzws + zdt * ( MAX( zWui, 0._wp ) - MIN( zWus, 0._wp ) )

[jchanut]

In 11281:

Error: Failed to load processor CommitTicketReference

No macro or processor named 'CommitTicketReference' found

[jchanut]

In 11282:

Error: Failed to load processor CommitTicketReference

No macro or processor named 'CommitTicketReference' found