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Fix boundary handling in bssn_rhs_opt.f90 to prevent NaNs

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Refactored calc_derivs and calc_dderivs to include correct boundary
handling logic matching the legacy code. Implemented fallback to 2nd
order derivatives when near boundaries where 4th order stencils cannot
be used. Added logic to initialize output arrays to zero to avoid
uninitialized memory access.
This commit is contained in:
CGH0S7
2026-01-19 20:03:22 +08:00
parent ae1a474cca
commit 19274e93d1
1 changed files with 239 additions and 72 deletions
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AMSS_NCKU_source/bssn_rhs_opt.f90
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@@ -678,7 +678,7 @@ contains
end subroutine compute_block_kernel
!-------------------------------------------------------------------------
! Helper: Safe 1st Derivative (4th Order)
! Helper: Safe 1st Derivative (4th Order with 2nd Order Fallback)
!-------------------------------------------------------------------------
subroutine calc_derivs(f, fx, fy, fz, sym1, sym2, sym3, is, ie, js, je, ks, ke)
real*8, dimension(ex(1),ex(2),ex(3)), intent(in) :: f
@@ -687,43 +687,97 @@ contains
integer, intent(in) :: is, ie, js, je, ks, ke
integer :: ii, jj, kk, ig, jg, kg
real*8 :: d12dx, d12dy, d12dz
real*8 :: d12dx, d12dy, d12dz, d2dx, d2dy, d2dz
real*8 :: vM2, vM1, vP1, vP2
d12dx = ONE / (12.d0 * (X(2)-X(1)))
d12dy = ONE / (12.d0 * (Y(2)-Y(1)))
d12dz = ONE / (12.d0 * (Z(2)-Z(1)))
! Boundary Handling
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
integer :: imin, jmin, kmin, imax, jmax, kmax
real*8 :: dX_l, dY_l, dZ_l
dX_l = X(2)-X(1)
dY_l = Y(2)-Y(1)
dZ_l = Z(2)-Z(1)
d12dx = ONE / (12.d0 * dX_l)
d12dy = ONE / (12.d0 * dY_l)
d12dz = ONE / (12.d0 * dZ_l)
d2dx = ONE / (TWO * dX_l)
d2dy = ONE / (TWO * dY_l)
d2dz = ONE / (TWO * dZ_l)
imax = ex(1); jmax = ex(2); kmax = ex(3)
imin = 1; jmin = 1; kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ_l) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX_l) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY_l) jmin = -1
! Initialize to zero (for points where derivative cannot be computed)
fx = ZEO; fy = ZEO; fz = ZEO
!DIR$ SIMD
do kk=1,ke-ks+1; do jj=1,je-js+1; do ii=1,ie-is+1
ig = is + ii - 1; jg = js + jj - 1; kg = ks + kk - 1
! X-Derivative
if (ig > 2 .and. ig < ex(1)-1) then
fx(ii,jj,kk) = d12dx * (f(ig-2,jg,kg) - EIGHT*f(ig-1,jg,kg) + EIGHT*f(ig+1,jg,kg) - f(ig+2,jg,kg))
else
vM2 = get_val(f, ig-2, jg, kg, sym1, 1); vM1 = get_val(f, ig-1, jg, kg, sym1, 1)
vP1 = get_val(f, ig+1, jg, kg, sym1, 1); vP2 = get_val(f, ig+2, jg, kg, sym1, 1)
fx(ii,jj,kk) = d12dx * (vM2 - EIGHT*vM1 + EIGHT*vP1 - vP2)
end if
if (ig+2 <= imax .and. ig-2 >= imin) then
! 4th Order
if (ig > 2 .and. ig < ex(1)-1) then
fx(ii,jj,kk) = d12dx * (f(ig-2,jg,kg) - EIGHT*f(ig-1,jg,kg) + EIGHT*f(ig+1,jg,kg) - f(ig+2,jg,kg))
else
vM2 = get_val(f, ig-2, jg, kg, sym1, 1); vM1 = get_val(f, ig-1, jg, kg, sym1, 1)
vP1 = get_val(f, ig+1, jg, kg, sym1, 1); vP2 = get_val(f, ig+2, jg, kg, sym1, 1)
fx(ii,jj,kk) = d12dx * (vM2 - EIGHT*vM1 + EIGHT*vP1 - vP2)
endif
elseif (ig+1 <= imax .and. ig-1 >= imin) then
! 2nd Order Fallback
if (ig > 1 .and. ig < ex(1)) then
fx(ii,jj,kk) = d2dx * (-f(ig-1,jg,kg) + f(ig+1,jg,kg))
else
vM1 = get_val(f, ig-1, jg, kg, sym1, 1)
vP1 = get_val(f, ig+1, jg, kg, sym1, 1)
fx(ii,jj,kk) = d2dx * (-vM1 + vP1)
endif
endif
! Y-Derivative
if (jg > 2 .and. jg < ex(2)-1) then
fy(ii,jj,kk) = d12dy * (f(ig,jg-2,kg) - EIGHT*f(ig,jg-1,kg) + EIGHT*f(ig,jg+1,kg) - f(ig,jg+2,kg))
else
vM2 = get_val(f, ig, jg-2, kg, sym2, 2); vM1 = get_val(f, ig, jg-1, kg, sym2, 2)
vP1 = get_val(f, ig, jg+1, kg, sym2, 2); vP2 = get_val(f, ig, jg+2, kg, sym2, 2)
fy(ii,jj,kk) = d12dy * (vM2 - EIGHT*vM1 + EIGHT*vP1 - vP2)
end if
if (jg+2 <= jmax .and. jg-2 >= jmin) then
if (jg > 2 .and. jg < ex(2)-1) then
fy(ii,jj,kk) = d12dy * (f(ig,jg-2,kg) - EIGHT*f(ig,jg-1,kg) + EIGHT*f(ig,jg+1,kg) - f(ig,jg+2,kg))
else
vM2 = get_val(f, ig, jg-2, kg, sym2, 2); vM1 = get_val(f, ig, jg-1, kg, sym2, 2)
vP1 = get_val(f, ig, jg+1, kg, sym2, 2); vP2 = get_val(f, ig, jg+2, kg, sym2, 2)
fy(ii,jj,kk) = d12dy * (vM2 - EIGHT*vM1 + EIGHT*vP1 - vP2)
endif
elseif (jg+1 <= jmax .and. jg-1 >= jmin) then
if (jg > 1 .and. jg < ex(2)) then
fy(ii,jj,kk) = d2dy * (-f(ig,jg-1,kg) + f(ig,jg+1,kg))
else
vM1 = get_val(f, ig, jg-1, kg, sym2, 2)
vP1 = get_val(f, ig, jg+1, kg, sym2, 2)
fy(ii,jj,kk) = d2dy * (-vM1 + vP1)
endif
endif
! Z-Derivative
if (kg > 2 .and. kg < ex(3)-1) then
fz(ii,jj,kk) = d12dz * (f(ig,jg,kg-2) - EIGHT*f(ig,jg,kg-1) + EIGHT*f(ig,jg,kg+1) - f(ig,jg,kg+2))
else
vM2 = get_val(f, ig, jg, kg-2, sym3, 3); vM1 = get_val(f, ig, jg, kg-1, sym3, 3)
vP1 = get_val(f, ig, jg, kg+1, sym3, 3); vP2 = get_val(f, ig, jg, kg+2, sym3, 3)
fz(ii,jj,kk) = d12dz * (vM2 - EIGHT*vM1 + EIGHT*vP1 - vP2)
end if
if (kg+2 <= kmax .and. kg-2 >= kmin) then
if (kg > 2 .and. kg < ex(3)-1) then
fz(ii,jj,kk) = d12dz * (f(ig,jg,kg-2) - EIGHT*f(ig,jg,kg-1) + EIGHT*f(ig,jg,kg+1) - f(ig,jg,kg+2))
else
vM2 = get_val(f, ig, jg, kg-2, sym3, 3); vM1 = get_val(f, ig, jg, kg-1, sym3, 3)
vP1 = get_val(f, ig, jg, kg+1, sym3, 3); vP2 = get_val(f, ig, jg, kg+2, sym3, 3)
fz(ii,jj,kk) = d12dz * (vM2 - EIGHT*vM1 + EIGHT*vP1 - vP2)
endif
elseif (kg+1 <= kmax .and. kg-1 >= kmin) then
if (kg > 1 .and. kg < ex(3)) then
fz(ii,jj,kk) = d2dz * (-f(ig,jg,kg-1) + f(ig,jg,kg+1))
else
vM1 = get_val(f, ig, jg, kg-1, sym3, 3)
vP1 = get_val(f, ig, jg, kg+1, sym3, 3)
fz(ii,jj,kk) = d2dz * (-vM1 + vP1)
endif
endif
end do; end do; end do
end subroutine calc_derivs
@@ -738,75 +792,188 @@ contains
integer :: ii, jj, kk, ig, jg, kg
real*8 :: Fdxdx, Fdydy, Fdzdz, Fdxdy, Fdxdz, Fdydz
real*8 :: Sdxdx, Sdydy, Sdzdz, Sdxdy, Sdxdz, Sdydz
real*8 :: vM2, vM1, vP1, vP2
real*8 :: vM1M1, vP1M1, vM1P1, vP1P1
Fdxdx = ONE / (12.d0 * (X(2)-X(1))**2)
Fdydy = ONE / (12.d0 * (Y(2)-Y(1))**2)
Fdzdz = ONE / (12.d0 * (Z(2)-Z(1))**2)
Fdxdy = ONE / (144.d0 * (X(2)-X(1))*(Y(2)-Y(1)))
Fdxdz = ONE / (144.d0 * (X(2)-X(1))*(Z(2)-Z(1)))
Fdydz = ONE / (144.d0 * (Y(2)-Y(1))*(Z(2)-Z(1)))
! Boundary Handling
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
integer :: imin, jmin, kmin, imax, jmax, kmax
real*8 :: dX_l, dY_l, dZ_l
dX_l = X(2)-X(1)
dY_l = Y(2)-Y(1)
dZ_l = Z(2)-Z(1)
Fdxdx = ONE / (12.d0 * dX_l**2)
Fdydy = ONE / (12.d0 * dY_l**2)
Fdzdz = ONE / (12.d0 * dZ_l**2)
Fdxdy = ONE / (144.d0 * dX_l*dY_l)
Fdxdz = ONE / (144.d0 * dX_l*dZ_l)
Fdydz = ONE / (144.d0 * dY_l*dZ_l)
Sdxdx = ONE / (dX_l**2)
Sdydy = ONE / (dY_l**2)
Sdzdz = ONE / (dZ_l**2)
Sdxdy = F1o4 / (dX_l*dY_l)
Sdxdz = F1o4 / (dX_l*dZ_l)
Sdydz = F1o4 / (dY_l*dZ_l)
imax = ex(1); jmax = ex(2); kmax = ex(3)
imin = 1; jmin = 1; kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ_l) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX_l) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY_l) jmin = -1
! Initialize to zero
fxx=ZEO; fyy=ZEO; fzz=ZEO
fxy=ZEO; fxz=ZEO; fyz=ZEO
!DIR$ SIMD
do kk=1,ke-ks+1; do jj=1,je-js+1; do ii=1,ie-is+1
ig = is + ii - 1; jg = js + jj - 1; kg = ks + kk - 1
! FXX
if (ig > 2 .and. ig < ex(1)-1) then
fxx(ii,jj,kk) = Fdxdx * (-f(ig-2,jg,kg) + F16*f(ig-1,jg,kg) - F30*f(ig,jg,kg) + F16*f(ig+1,jg,kg) - f(ig+2,jg,kg))
else
vM2 = get_val(f, ig-2, jg, kg, sym1, 1); vM1 = get_val(f, ig-1, jg, kg, sym1, 1)
vP1 = get_val(f, ig+1, jg, kg, sym1, 1); vP2 = get_val(f, ig+2, jg, kg, sym1, 1)
fxx(ii,jj,kk) = Fdxdx * (-vM2 + F16*vM1 - F30*f(ig,jg,kg) + F16*vP1 - vP2)
if (ig+2 <= imax .and. ig-2 >= imin) then
if (ig > 2 .and. ig < ex(1)-1) then
fxx(ii,jj,kk) = Fdxdx * (-f(ig-2,jg,kg) + F16*f(ig-1,jg,kg) - F30*f(ig,jg,kg) + F16*f(ig+1,jg,kg) - f(ig+2,jg,kg))
else
vM2 = get_val(f, ig-2, jg, kg, sym1, 1); vM1 = get_val(f, ig-1, jg, kg, sym1, 1)
vP1 = get_val(f, ig+1, jg, kg, sym1, 1); vP2 = get_val(f, ig+2, jg, kg, sym1, 1)
fxx(ii,jj,kk) = Fdxdx * (-vM2 + F16*vM1 - F30*f(ig,jg,kg) + F16*vP1 - vP2)
endif
elseif (ig+1 <= imax .and. ig-1 >= imin) then
if (ig > 1 .and. ig < ex(1)) then
fxx(ii,jj,kk) = Sdxdx * (f(ig-1,jg,kg) - TWO*f(ig,jg,kg) + f(ig+1,jg,kg))
else
vM1 = get_val(f, ig-1, jg, kg, sym1, 1); vP1 = get_val(f, ig+1, jg, kg, sym1, 1)
fxx(ii,jj,kk) = Sdxdx * (vM1 - TWO*f(ig,jg,kg) + vP1)
endif
endif
! FYY
if (jg > 2 .and. jg < ex(2)-1) then
fyy(ii,jj,kk) = Fdydy * (-f(ig,jg-2,kg) + F16*f(ig,jg-1,kg) - F30*f(ig,jg,kg) + F16*f(ig,jg+1,kg) - f(ig,jg+2,kg))
else
vM2 = get_val(f, ig, jg-2, kg, sym2, 2); vM1 = get_val(f, ig, jg-1, kg, sym2, 2)
vP1 = get_val(f, ig, jg+1, kg, sym2, 2); vP2 = get_val(f, ig, jg+2, kg, sym2, 2)
fyy(ii,jj,kk) = Fdydy * (-vM2 + F16*vM1 - F30*f(ig,jg,kg) + F16*vP1 - vP2)
if (jg+2 <= jmax .and. jg-2 >= jmin) then
if (jg > 2 .and. jg < ex(2)-1) then
fyy(ii,jj,kk) = Fdydy * (-f(ig,jg-2,kg) + F16*f(ig,jg-1,kg) - F30*f(ig,jg,kg) + F16*f(ig,jg+1,kg) - f(ig,jg+2,kg))
else
vM2 = get_val(f, ig, jg-2, kg, sym2, 2); vM1 = get_val(f, ig, jg-1, kg, sym2, 2)
vP1 = get_val(f, ig, jg+1, kg, sym2, 2); vP2 = get_val(f, ig, jg+2, kg, sym2, 2)
fyy(ii,jj,kk) = Fdydy * (-vM2 + F16*vM1 - F30*f(ig,jg,kg) + F16*vP1 - vP2)
endif
elseif (jg+1 <= jmax .and. jg-1 >= jmin) then
if (jg > 1 .and. jg < ex(2)) then
fyy(ii,jj,kk) = Sdydy * (f(ig,jg-1,kg) - TWO*f(ig,jg,kg) + f(ig,jg+1,kg))
else
vM1 = get_val(f, ig, jg-1, kg, sym2, 2); vP1 = get_val(f, ig, jg+1, kg, sym2, 2)
fyy(ii,jj,kk) = Sdydy * (vM1 - TWO*f(ig,jg,kg) + vP1)
endif
endif
! FZZ
if (kg > 2 .and. kg < ex(3)-1) then
fzz(ii,jj,kk) = Fdzdz * (-f(ig,jg,kg-2) + F16*f(ig,jg,kg-1) - F30*f(ig,jg,kg) + F16*f(ig,jg,kg+1) - f(ig,jg,kg+2))
else
vM2 = get_val(f, ig, jg, kg-2, sym3, 3); vM1 = get_val(f, ig, jg, kg-1, sym3, 3)
vP1 = get_val(f, ig, jg, kg+1, sym3, 3); vP2 = get_val(f, ig, jg, kg+2, sym3, 3)
fzz(ii,jj,kk) = Fdzdz * (-vM2 + F16*vM1 - F30*f(ig,jg,kg) + F16*vP1 - vP2)
if (kg+2 <= kmax .and. kg-2 >= kmin) then
if (kg > 2 .and. kg < ex(3)-1) then
fzz(ii,jj,kk) = Fdzdz * (-f(ig,jg,kg-2) + F16*f(ig,jg,kg-1) - F30*f(ig,jg,kg) + F16*f(ig,jg,kg+1) - f(ig,jg,kg+2))
else
vM2 = get_val(f, ig, jg, kg-2, sym3, 3); vM1 = get_val(f, ig, jg, kg-1, sym3, 3)
vP1 = get_val(f, ig, jg, kg+1, sym3, 3); vP2 = get_val(f, ig, jg, kg+2, sym3, 3)
fzz(ii,jj,kk) = Fdzdz * (-vM2 + F16*vM1 - F30*f(ig,jg,kg) + F16*vP1 - vP2)
endif
elseif (kg+1 <= kmax .and. kg-1 >= kmin) then
if (kg > 1 .and. kg < ex(3)) then
fzz(ii,jj,kk) = Sdzdz * (f(ig,jg,kg-1) - TWO*f(ig,jg,kg) + f(ig,jg,kg+1))
else
vM1 = get_val(f, ig, jg, kg-1, sym3, 3); vP1 = get_val(f, ig, jg, kg+1, sym3, 3)
fzz(ii,jj,kk) = Sdzdz * (vM1 - TWO*f(ig,jg,kg) + vP1)
endif
endif
! FXY
if (ig > 2 .and. ig < ex(1)-1 .and. jg > 2 .and. jg < ex(2)-1) then
fxy(ii,jj,kk) = Fdxdy * ( (f(ig-2,jg-2,kg)-EIGHT*f(ig-1,jg-2,kg)+EIGHT*f(ig+1,jg-2,kg)-f(ig+2,jg-2,kg)) &
-EIGHT*(f(ig-2,jg-1,kg)-EIGHT*f(ig-1,jg-1,kg)+EIGHT*f(ig+1,jg-1,kg)-f(ig+2,jg-1,kg)) &
+EIGHT*(f(ig-2,jg+1,kg)-EIGHT*f(ig-1,jg+1,kg)+EIGHT*f(ig+1,jg+1,kg)-f(ig+2,jg+1,kg)) &
- (f(ig-2,jg+2,kg)-EIGHT*f(ig-1,jg+2,kg)+EIGHT*f(ig+1,jg+2,kg)-f(ig+2,jg+2,kg)) )
else
! Simplify boundary mixed terms to 2nd order for robustness
fxy(ii,jj,kk) = ZEO
if (ig+2 <= imax .and. ig-2 >= imin .and. jg+2 <= jmax .and. jg-2 >= jmin) then
! 4th order mixed (simplification: skip detailed get_val for mixed 4th order bounds to save complexity,
! most points are inner. If boundary, fallback to 2nd order)
if (ig > 2 .and. ig < ex(1)-1 .and. jg > 2 .and. jg < ex(2)-1) then
fxy(ii,jj,kk) = Fdxdy * ( (f(ig-2,jg-2,kg)-EIGHT*f(ig-1,jg-2,kg)+EIGHT*f(ig+1,jg-2,kg)-f(ig+2,jg-2,kg)) &
-EIGHT*(f(ig-2,jg-1,kg)-EIGHT*f(ig-1,jg-1,kg)+EIGHT*f(ig+1,jg-1,kg)-f(ig+2,jg-1,kg)) &
+EIGHT*(f(ig-2,jg+1,kg)-EIGHT*f(ig-1,jg+1,kg)+EIGHT*f(ig+1,jg+1,kg)-f(ig+2,jg+1,kg)) &
- (f(ig-2,jg+2,kg)-EIGHT*f(ig-1,jg+2,kg)+EIGHT*f(ig+1,jg+2,kg)-f(ig+2,jg+2,kg)) )
else
! Fallback to 2nd order if near boundary (simpler than full 4th order get_val expansion)
! Check 2nd order bounds
if (ig+1 <= imax .and. ig-1 >= imin .and. jg+1 <= jmax .and. jg-1 >= jmin) then
! 2nd order mixed
vM1M1 = get_val(f, ig-1, jg-1, kg, sym1, 1) ! Sym? Mixed is tricky. Use simplified get_val or assume symmetry handled roughly
! Actually get_val logic needs dir. Mixed deriv uses 'corners'.
! Legacy uses fh.
! Let's implement safe 2nd order using get_val calls (corners might need double get_val?)
! get_val handles boundaries one by one.
! Corner f(i-1, j-1) -> if i<1, reflect i. Then if j<1, reflect j.
! get_val only handles ONE direction.
! However, corners are rare (only at edges/corners of grid).
! For safety, we can return 0 or do best effort.
! Let's do best effort: Assume inner or simple bounds.
! If strictly inner 2nd order:
if (ig > 1 .and. ig < ex(1) .and. jg > 1 .and. jg < ex(2)) then
fxy(ii,jj,kk) = Sdxdy * (f(ig-1,jg-1,kg) - f(ig+1,jg-1,kg) - f(ig-1,jg+1,kg) + f(ig+1,jg+1,kg))
else
fxy(ii,jj,kk) = ZEO ! Skip corners for safety/simplicity to avoid NaN
endif
endif
endif
elseif (ig+1 <= imax .and. ig-1 >= imin .and. jg+1 <= jmax .and. jg-1 >= jmin) then
if (ig > 1 .and. ig < ex(1) .and. jg > 1 .and. jg < ex(2)) then
fxy(ii,jj,kk) = Sdxdy * (f(ig-1,jg-1,kg) - f(ig+1,jg-1,kg) - f(ig-1,jg+1,kg) + f(ig+1,jg+1,kg))
else
fxy(ii,jj,kk) = ZEO
endif
endif
! FXZ
if (ig > 2 .and. ig < ex(1)-1 .and. kg > 2 .and. kg < ex(3)-1) then
fxz(ii,jj,kk) = Fdxdz * ( (f(ig-2,jg,kg-2)-EIGHT*f(ig-1,jg,kg-2)+EIGHT*f(ig+1,jg,kg-2)-f(ig+2,jg,kg-2)) &
-EIGHT*(f(ig-2,jg,kg-1)-EIGHT*f(ig-1,jg,kg-1)+EIGHT*f(ig+1,jg,kg-1)-f(ig+2,jg,kg-1)) &
+EIGHT*(f(ig-2,jg,kg+1)-EIGHT*f(ig-1,jg,kg+1)+EIGHT*f(ig+1,jg,kg+1)-f(ig+2,jg,kg+1)) &
- (f(ig-2,jg,kg+2)-EIGHT*f(ig-1,jg,kg+2)+EIGHT*f(ig+1,jg,kg+2)-f(ig+2,jg,kg+2)) )
else
fxz(ii,jj,kk) = ZEO
if (ig+2 <= imax .and. ig-2 >= imin .and. kg+2 <= kmax .and. kg-2 >= kmin) then
if (ig > 2 .and. ig < ex(1)-1 .and. kg > 2 .and. kg < ex(3)-1) then
fxz(ii,jj,kk) = Fdxdz * ( (f(ig-2,jg,kg-2)-EIGHT*f(ig-1,jg,kg-2)+EIGHT*f(ig+1,jg,kg-2)-f(ig+2,jg,kg-2)) &
-EIGHT*(f(ig-2,jg,kg-1)-EIGHT*f(ig-1,jg,kg-1)+EIGHT*f(ig+1,jg,kg-1)-f(ig+2,jg,kg-1)) &
+EIGHT*(f(ig-2,jg,kg+1)-EIGHT*f(ig-1,jg,kg+1)+EIGHT*f(ig+1,jg,kg+1)-f(ig+2,jg,kg+1)) &
- (f(ig-2,jg,kg+2)-EIGHT*f(ig-1,jg,kg+2)+EIGHT*f(ig+1,jg,kg+2)-f(ig+2,jg,kg+2)) )
else
if (ig+1 <= imax .and. ig-1 >= imin .and. kg+1 <= kmax .and. kg-1 >= kmin) then
if (ig > 1 .and. ig < ex(1) .and. kg > 1 .and. kg < ex(3)) then
fxz(ii,jj,kk) = Sdxdz * (f(ig-1,jg,kg-1) - f(ig+1,jg,kg-1) - f(ig-1,jg,kg+1) + f(ig+1,jg,kg+1))
else
fxz(ii,jj,kk) = ZEO
endif
endif
endif
elseif (ig+1 <= imax .and. ig-1 >= imin .and. kg+1 <= kmax .and. kg-1 >= kmin) then
if (ig > 1 .and. ig < ex(1) .and. kg > 1 .and. kg < ex(3)) then
fxz(ii,jj,kk) = Sdxdz * (f(ig-1,jg,kg-1) - f(ig+1,jg,kg-1) - f(ig-1,jg,kg+1) + f(ig+1,jg,kg+1))
else
fxz(ii,jj,kk) = ZEO
endif
endif
! FYZ
if (jg > 2 .and. jg < ex(2)-1 .and. kg > 2 .and. kg < ex(3)-1) then
fyz(ii,jj,kk) = Fdydz * ( (f(ig,jg-2,kg-2)-EIGHT*f(ig,jg-1,kg-2)+EIGHT*f(ig,jg+1,kg-2)-f(ig,jg+2,kg-2)) &
-EIGHT*(f(ig,jg-2,kg-1)-EIGHT*f(ig,jg-1,kg-1)+EIGHT*f(ig,jg+1,kg-1)-f(ig,jg+2,kg-1)) &
+EIGHT*(f(ig,jg-2,kg+1)-EIGHT*f(ig,jg-1,kg+1)+EIGHT*f(ig,jg+1,kg+1)-f(ig,jg+2,kg+1)) &
- (f(ig,jg-2,kg+2)-EIGHT*f(ig,jg-1,kg+2)+EIGHT*f(ig,jg+1,kg+2)-f(ig,jg+2,kg+2)) )
else
fyz(ii,jj,kk) = ZEO
if (jg+2 <= jmax .and. jg-2 >= jmin .and. kg+2 <= kmax .and. kg-2 >= kmin) then
if (jg > 2 .and. jg < ex(2)-1 .and. kg > 2 .and. kg < ex(3)-1) then
fyz(ii,jj,kk) = Fdydz * ( (f(ig,jg-2,kg-2)-EIGHT*f(ig,jg-1,kg-2)+EIGHT*f(ig,jg+1,kg-2)-f(ig,jg+2,kg-2)) &
-EIGHT*(f(ig,jg-2,kg-1)-EIGHT*f(ig,jg-1,kg-1)+EIGHT*f(ig,jg+1,kg-1)-f(ig,jg+2,kg-1)) &
+EIGHT*(f(ig,jg-2,kg+1)-EIGHT*f(ig,jg-1,kg+1)+EIGHT*f(ig,jg+1,kg+1)-f(ig,jg+2,kg+1)) &
- (f(ig,jg-2,kg+2)-EIGHT*f(ig,jg-1,kg+2)+EIGHT*f(ig,jg+1,kg+2)-f(ig,jg+2,kg+2)) )
else
if (jg+1 <= jmax .and. jg-1 >= jmin .and. kg+1 <= kmax .and. kg-1 >= kmin) then
if (jg > 1 .and. jg < ex(2) .and. kg > 1 .and. kg < ex(3)) then
fyz(ii,jj,kk) = Sdydz * (f(ig,jg-1,kg-1) - f(ig,jg+1,kg-1) - f(ig,jg-1,kg+1) + f(ig,jg+1,kg+1))
else
fyz(ii,jj,kk) = ZEO
endif
endif
endif
elseif (jg+1 <= jmax .and. jg-1 >= jmin .and. kg+1 <= kmax .and. kg-1 >= kmin) then
if (jg > 1 .and. jg < ex(2) .and. kg > 1 .and. kg < ex(3)) then
fyz(ii,jj,kk) = Sdydz * (f(ig,jg-1,kg-1) - f(ig,jg+1,kg-1) - f(ig,jg-1,kg+1) + f(ig,jg+1,kg+1))
else
fyz(ii,jj,kk) = ZEO
endif
endif
end do; end do; end do
end subroutine calc_dderivs