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 Post subject: about the implicit upstream radiation conditionPosted: Wed Mar 28, 2018 8:02 am

Joined: Fri Sep 11, 2009 1:48 pm
Posts: 57
Location: nmefc
Hello all,
I have derived the implicit upstream radiation condition from Marchesiello et al.(2001). I found it should have an implicit assumption dx=dy (or om=on in ROMS). If not, the variables r_x (Cx in ROMS) and r_y (Cy in ROMS) should be
Code:
dy*dy*dudt*dudx*alpha                           dx*dx*dudt*dudy*beta
r_x= -  ---------------------------------       r_y= -   ---------------------------------
dy*dy*dudx*dudx+dx*dx*dudy*dudy                   dy*dy*dudx*dudx+dx*dx*dudy*dudy

x(b-1,j)-x(b-2,j)             y(b-1,j)-y(b-1,j-1)
alpha= -------------------     beta=---------------------
x(b,j)-x(b-1,j)                 y(b,j)-y(b,j-1)

Then, I think the file u3_dbc_im.F should be changed for the western boundary condition as followed,
Code:
dxzxm=GRID(ng)%om_r(Istr+1,j))
aphazxm=dxzxm/GRID(ng)%om_r(Istr,j)

IF ((dUdt*dUdx).lt.0.0_r8) dUdt=0.0_r8
dyzxm=GRID(ng)%on_p(Istr+1,j))
betazxm=dyzxm/GRID(ng)%on_p(Istr,j)
ELSE
dyzxm=GRID(ng)%on_p(Istr+1,j+1))
betazxm=dyzxm/GRID(ng)%on_p(Istr,j+1)
END IF
!!                cff=MAX(dUdx*dUdx+dUde*dUde,eps)
!!                Cx=dUdt*dUdx
cff=MAX(dyzxm*dyzxm*dUdx*dUdx+dxzxm*dxzxm*dUde*dUde,eps)
Cx=dUdt*dUdx*dyzxm*dyzxm*aphazxm
Ce=MIN(cff,MAX(dUdt*dUde,-cff))*dxzxm*dxzxm*betazxm
# else
Ce=0.0_r8
# endif

Do you think it is a bug for ROMS? Do I have changed it correct? Which subindex (i,i-1,i+1, j,j+1 et al.) or variables (om_r, om_u, om_p) should I use? How about for other ones, such as eastern, southern and northern conditions?

By the way, this is also the reason I have posted on the title "question about the caculating of om_p, om_u, on_p, on_u" in https://www.myroms.org/forum/viewtopic.php?t=4805

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