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gad_pqm_flx_r.F
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gad_pqm_flx_r.F
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# include "GAD_OPTIONS.h"
SUBROUTINE GAD_PQM_FLX_R(bi,bj,ix,iy,
& delT,wvel,wfac,
& fhat,flux,myThid)
C |================================================================|
C | PQM_FLX_R: evaluate PQM flux on grid-cell edges. |
C |================================================================|
implicit none
C =============================================== global variables
# include "SIZE.h"
# include "GRID.h"
# include "GAD.h"
C ================================================================
C bi,bj :: tile indexing.
C ix :: x-index.
C iy :: y-index.
C delT :: time-step.
C wvel :: vel.-comp in r-direction.
C wfac :: vel.-flux in r-direction.
C fhat :: row of poly. coeff.
C flux :: adv.-flux in r-direction.
C myThid :: thread number.
C ================================================================
integer bi,bj,ix,iy
_RL delT(1:Nr)
_RL wvel(1-OLx:sNx+OLx,
& 1-OLy:sNy+OLy,
& 1:Nr)
_RL wfac(1-OLx:sNx+OLx,
& 1-OLy:sNy+OLy,
& 1:Nr)
_RL fhat(1:5 ,
& 1:Nr)
_RL flux(1-OLx:sNx+OLx,
& 1-OLy:sNy+OLy,
& 1:Nr)
integer myThid
C ================================================================
C ir :: r-indexing.
C wCFL :: CFL number.
C intF :: upwind tracer edge-value.
C ss11,ss22 :: int. endpoints.
C ivec :: int. basis vec.
C ================================================================
integer ir
_RL wCFL,intF
_RL ss11,ss22
_RL ivec(1:5)
C ================================================================
C (1): calc. "departure-points" for each grid-cell edge by int-
C egrating edge position backward in time over one single
C time-step. This is a "single-cell" implementation: requ-
C ires CFL <= 1.0.
C (2): calc. flux as the integral of the upwind grid-cell poly-
C nomial over the deformation interval found in (1).
C ================================================================
do ir = +2, Nr
if (wfac(ix,iy,ir) .eq. 0. _d 0) then
flux(ix,iy,ir) = 0. _d 0
else
if (wfac(ix,iy,ir) .lt. 0. _d 0) then
C ==================== integrate PQM profile over upwind cell IR-1
wCFL = wvel(ix,iy,ir)
& * delT(ir-1)*recip_drF(ir-1)
ss11 = +1. _d 0 + 2. _d 0 * wCFL
ss22 = +1. _d 0
C ==================== integrate profile over region swept by face
ivec(1) = ss22 - ss11
ivec(2) =(ss22 ** 2
& - ss11 ** 2)*(1. _d 0 / 2. _d 0)
ivec(3) =(ss22 ** 3
& - ss11 ** 3)*(1. _d 0 / 3. _d 0)
ivec(4) =(ss22 ** 4
& - ss11 ** 4)*(1. _d 0 / 4. _d 0)
ivec(5) =(ss22 ** 5
& - ss11 ** 5)*(1. _d 0 / 5. _d 0)
intF = ivec(1) * fhat(1,ir-1)
& + ivec(2) * fhat(2,ir-1)
& + ivec(3) * fhat(3,ir-1)
& + ivec(4) * fhat(4,ir-1)
& + ivec(5) * fhat(5,ir-1)
CML intF = intF / (ss22 - ss11)
else
C ==================== integrate PQM profile over upwind cell IR+0
wCFL = wvel(ix,iy,ir)
& * delT(ir-0)*recip_drF(ir-0)
ss11 = -1. _d 0 + 2. _d 0 * wCFL
ss22 = -1. _d 0
C ==================== integrate profile over region swept by face
ivec(1) = ss22 - ss11
ivec(2) =(ss22 ** 2
& - ss11 ** 2)*(1. _d 0 / 2. _d 0)
ivec(3) =(ss22 ** 3
& - ss11 ** 3)*(1. _d 0 / 3. _d 0)
ivec(4) =(ss22 ** 4
& - ss11 ** 4)*(1. _d 0 / 4. _d 0)
ivec(5) =(ss22 ** 5
& - ss11 ** 5)*(1. _d 0 / 5. _d 0)
intF = ivec(1) * fhat(1,ir-0)
& + ivec(2) * fhat(2,ir-0)
& + ivec(3) * fhat(3,ir-0)
& + ivec(4) * fhat(4,ir-0)
& + ivec(5) * fhat(5,ir-0)
CML intF = intF / (ss22 - ss11)
end if
c intF = -0.5 _d 0 * intF / wCFL
C- to avoid potential underflow:
intF = -0.5 _d 0 * intF/sign(max(abs(wCFL),1.d-20),wCFL)
C ==================== calc. flux = upwind tracer * face-transport
flux(ix,iy,ir) = + wfac(ix,iy,ir) * intF
end if
end do
return
c end subroutine GAD_PQM_FLX_R
end