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! version 3; Last Modified: May 7, 2008.
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***s/r nli - compute nonlinear portion of governing & derived equations
*
#include "model_macros_f.h"
*
subroutine nli() 1,1
*
implicit none
*
*authors
* Alain Patoine & Gabriel Lemay
*
*revision
* v2_00 - Desgagne M. - initial MPI version (from rhs v1_03)
* v2_30 - Edouard S. - adapt for vertical hybrid coordinate
* add Ncn
* v3_00 - Desgagne & Lee - Lam configuration
*
*object
*******************************************************************************
* *
* Define the nonlinear perturbation of the logarithmic hydrostatic pressure *
* *
* / pi' \ pi'lin *
* q" = ln | 1 + --- | - ------ where pi'lin = b * s *
* \ z / z *
* _____________________ *
* | | *
* the nonlinear deviation of the horizontal | NONHYDROSTATIC ONLY | *
* momentum equations are then written as |_____________________| *
* *
* | *
* R / \ | 1 *
* d | dq dq" | | dphi *
* N = ---- | T' ---- + T* ---- | + ---- (mu) ---- *
* U 2 | dx dx | | 2 dx *
* a \ / | a *
* | *
* | *
* R / \ | 1 *
* d | dq dq"| | dphi *
* N = ---- | T' C -- + T* C -- | + ---- (mu) C ---- *
* V 2 | dy dy | | 2 dy *
* a \ / | a *
* | *
* *
*******************************************************************************
* *
* / \ *
* | | *
* 1 | / \ | *
* | | /\b * ( exp(s)-1 ) | / /\b * s \ | *
* N = --- | ln | 1 + ------------------- | - | ----------- | | *
* cn tau | | /\A + /\b | \ /\A + /\b / | *
* | \ / | *
* \ / *
* *
* *
* where : /\ = d/d(eta) *
*******************************************************************************
* *
* Nonlinear deviation of horizontal divergence: *
* *
* 1 / dN dN \ *
* | U V | 1 *
* N = --- | ---- + C ---- | - --- N *
* 1 2 | | tau cn *
* C \ dx dy / *
* *
*******************************************************************************
* *
* Nonlinear deviation of thermodynamic equation (also recognized as N2): *
* *
* 1 / \ / T' \ T'lin *
* N = --- | - cappa q" + T" | where T" = ln | 1 + --- | - ----- *
* th tau \ / \ T* / T* *
* *
*******************************************************************************
* *
* Nonlinear deviation for vertical motion: *
* _____________________ *
* 1 / \ | | *
* N = --- | mu - mu | | NONHYDROSTATIC ONLY | *
* 3 tau \ lin / |_____________________| *
* *
*******************************************************************************
* _____________________ *
* We are now ready to calculate the | | *
* NONLINEAR RESIDUE of Helmholtz eqn: | NONHYDROSTATIC ONLY | *
* |_____________________| *
* | *
* | *
* / _z \+ gamma / ___z \- | gamma / ___z \- gamma / __z \+ *
* N = | N | + --------- | z N | + --------- | z N | + ----- | N' | *
* h \ 1 / cappa tau \ th / | cappa tau \ 3 / tau \ 3 / *
* | *
* | where *
* | R T* *
* | d *
* The involved operators are defined | N' = N - & ------------ N *
* as in Cote et al., 1990, M.W.R. 118, | 3 3 H 2 2 th *
* 2707-2717: | cappa g tau *
* *
* *
* / _z \+ P(k-1) + P(k) dz(k-1) P(k) + P(k+1) dz(k) *
* | P | = ------------- ------- + ------------- ----- *
* \ /k 2 2 2 2 *
* *
* / _z \- M(k-1) + M(k) M(k) + M(k+1) M(k-1) - M(k+1) *
* | M | = ------------- - ------------- = --------------- *
* \ /k 2 2 2 *
* *
* *
*******************************************************************************
* *
* 2 *
* (TOTAL RHS) = a ( R - N ) *
* h h *
* *
*******************************************************************************
*
*arguments
* none
*
*implicits
#include "glb_ld.cdk"
#include "lun.cdk"
#include "schm.cdk"
#include "p_geof.cdk"
#include "rhsc.cdk"
#include "nl.cdk"
#include "cori.cdk"
#include "vt0.cdk"
#include "vtx.cdk"
#include "ptopo.cdk"
#include "lctl.cdk"
*
*modules
integer vmmlod, vmmget, vmmuld
external vmmlod, vmmget, vmmuld
*
integer pnerr, pnlod, pnlkey1(14), i, j
real wijk1(LDIST_SHAPE,l_nk),wijk2(LDIST_SHAPE,l_nk)
real wk1(LDIST_SIZ*l_nk)
**
* __________________________________________________________________
*
*
if (Lun_debug_L) write(Lun_out,1000)
*
pnlkey1(1) = VMM_KEY(rheln)
pnlkey1(2) = VMM_KEY(rhell)
pnlkey1(3) = VMM_KEY(tpt0)
pnlkey1(4) = VMM_KEY(tplt0)
pnlkey1(5) = VMM_KEY(pipt0)
pnlkey1(6) = VMM_KEY(st0)
pnlkey1(7) = VMM_KEY(qt0)
pnlod =7
if (.not. Schm_hydro_L) then
pnlkey1(pnlod+1) = VMM_KEY(fipt0)
pnlkey1(pnlod+2) = VMM_KEY(topo)
pnlkey1(pnlod+3) = VMM_KEY(mut0)
pnlkey1(pnlod+4) = VMM_KEY(multx)
pnlod = pnlod+4
endif
if (Cori_cornl_L) then
pnlkey1(pnlod+1) = VMM_KEY(ut0)
pnlkey1(pnlod+2) = VMM_KEY(vt0)
pnlod = pnlod+2
endif
*
pnerr = vmmlod(pnlkey1,pnlod)
* - - - - - - - - - - - - - - -
pnerr = VMM_GET_VAR(rheln)
pnerr = VMM_GET_VAR(rhell)
pnerr = VMM_GET_VAR(tpt0)
pnerr = VMM_GET_VAR(tplt0)
pnerr = VMM_GET_VAR(pipt0)
pnerr = VMM_GET_VAR(st0)
pnerr = VMM_GET_VAR(qt0)
if (.not. Schm_hydro_L) then
pnerr = VMM_GET_VAR(fipt0)
pnerr = VMM_GET_VAR(topo)
pnerr = VMM_GET_VAR(mut0)
pnerr = VMM_GET_VAR(multx)
else
fipt0_ = 0
topo_ = 0
mut0_ = 0
multx_ = 0
endif
if (Cori_cornl_L) then
pnerr = VMM_GET_VAR(ut0)
pnerr = VMM_GET_VAR(vt0)
else
ut0_ = 0
vt0_ = 0
endif
*
c if (Acid_test_L) then tpt0,tplt0,pipt0,st0
c call glbstat (tpt0,'tpt0',LDIST_DIM,G_nk,8+acid_i0,G_ni-8-acid_in,
c % 8+acid_j0,G_nj-8-acid_jn,1,G_nk)
c call glbstat (st0,'st0',LDIST_DIM,1,8+acid_i0,G_ni-8-acid_in,
c % 8+acid_j0,G_nj-8-acid_jn,1,1)
c endif
*
call nlip_2 ( nl_nu, nl_nv, wk1, nl_nth, nl_n3, nl_n3p,
$ rheln, rhell, tpt0, tplt0, pipt0, nl_ncn,
$ st0, qt0, fipt0, topo, ut0, vt0, mut0, multx,
$ wijk1, wijk2, LDIST_DIM,l_nk )
*
*
c if (Acid_test_L) then nu,nv,nth,ncn
c call glbstat (nl_nu,'NU',LDIST_DIM,G_nk,8+acid_i0,G_ni-8-acid_in,
c % 8+acid_j0,G_nj-8-acid_jn,1,G_nk)
* The rheln sees future Ru,Rv so it will not match to the piloting run
c if (Lun_out.gt.0)
c % write(Lun_out,*)'Rheln has future Ru,Rv so no match to pilot run'
c call glbstat (rheln,'Rhln',LDIST_DIM,G_nk,8+acid_i0,G_ni-8-acid_in,
c % 8+acid_j0,G_nj-8-acid_jn,1,G_nk)
c endif
pnerr = vmmuld(-1,0)
*
1000 format(/,5X,'COMPUTE NON-LINEAR RHS: (S/R NLI)')
*
* __________________________________________________________________
*
return
end