about the implicit upstream radiation condition

[xiaozhu557]

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

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              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,

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     	  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
                IF ((dUdt*(grad(Istr+1,j  )+                            &
     &                     grad(Istr+1,j+1))).gt.0.0_r8) THEN
                  dUde=grad(Istr+1,j  )
	          dyzxm=GRID(ng)%on_p(Istr+1,j))
                  betazxm=dyzxm/GRID(ng)%on_p(Istr,j)
                ELSE
                  dUde=grad(Istr+1,j+1)
	          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
# ifdef RADIATION_2D
                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 viewtopic.php?t=4805