#include "cctk.h" #include "cctk_Functions.h" #include "cctk_Parameters.h" subroutine deriv_gf_4_3 ( var, ni, nj, nk, dir, bb, gsize, delta, dvar ) implicit none DECLARE_CCTK_FUNCTIONS DECLARE_CCTK_PARAMETERS CCTK_REAL, parameter :: zero = 0.0 integer, parameter :: wp = kind(zero) CCTK_INT, intent(IN) :: ni, nj, nk CCTK_REAL, dimension(ni,nj,nk), intent(IN) :: var CCTK_INT, intent(IN) :: dir CCTK_INT, intent(IN) :: bb(2) CCTK_INT, intent(IN) :: gsize CCTK_REAL, intent(IN) :: delta CCTK_REAL, dimension(ni,nj,nk), intent(OUT) :: dvar CCTK_REAL, dimension(2), save :: a CCTK_REAL, dimension(7,5), save :: q CCTK_REAL :: idel CCTK_REAL :: f0, f1, f2, f3 CCTK_INT :: il, ir, jl, jr, kl, kr logical, save :: first = .true. if ( first ) then a(1) = 2.0_wp/3.0_wp; a(2) = -1.0_wp/12.0_wp f0 = sqrt(26116897.0_wp) f1 = -56764003702447356523.0_wp + 8154993476273221.0_wp * f0 f2 = -55804550303.0_wp + 9650225.0_wp * f0 f3 = 3262210757.0_wp + 271861.0_wp * f0 q(1,1) = -11._wp/6.0_wp; q(2,1) = 3.0_wp q(3,1) = -3.0_wp/2.0_wp; q(4,1) = 1.0_wp/3.0_wp q(5,1) = zero; q(6,1) = zero; q(7,1) = zero q(1,2) = -24.0_wp * ( -779042810827742869.0_wp + & 104535124033147.0_wp * f0 ) / f1 q(2,2) = -( -176530817412806109689.0_wp + & 29768274816875927.0_wp * f0 ) / ( 6.0_wp * f1 ) q(3,2) = 343.0_wp * ( -171079116122226871.0_wp + & 27975630462649.0_wp * f0 ) / f1 q(4,2) = -3.0_wp * ( -7475554291248533227.0_wp + & 1648464218793925.0_wp * f0 ) / ( 2.0_wp * f1 ) q(5,2) = ( -2383792768180030915.0_wp + & 1179620587812973.0_wp * f0 ) / ( 3.0_wp * f1 ) q(6,2) = -1232.0_wp * ( -115724529581315.0_wp + 37280576429.0_wp * f0 ) / f1 q(7,2) = zero q(1,3) = -12.0_wp * ( -380966843.0_wp + 86315.0_wp * f0 ) / f2 q(2,3) = ( 5024933015.0_wp + 2010631.0_wp * f0 ) / ( 3.0_wp * f2 ) q(3,3) = -231.0_wp * ( -431968921.0_wp + 86711.0_wp * f0 ) / ( 2.0_wp * f2 ) q(4,3) = ( -65931742559.0_wp + 12256337.0_wp * f0 ) / f2 q(5,3) = -( -50597298167.0_wp + 9716873.0_wp * f0 ) / ( 6.0_wp * f2 ) q(6,3) = -88.0_wp * ( -15453061.0_wp + 2911.0_wp * f0 ) / f2 q(7,3) = zero q(1,4) = 48.0_wp * ( -56020909845192541.0_wp + & 9790180507043.0_wp * f0 ) / f1 q(2,4) = ( -9918249049237586011.0_wp + & 1463702013196501.0_wp * f0 ) / ( 6.0_wp * f1) q(3,4) = -13.0_wp * ( -4130451756851441723.0_wp + & 664278707201077.0_wp * f0 ) / f1 q(4,4) = 3.0_wp * ( -26937108467782666617.0_wp + & 5169063172799767.0_wp * f0 ) / ( 2.0_wp * f1 ) q(5,4) = -( 6548308508012371315.0_wp + & 3968886380989379.0_wp * f0 ) / ( 3.0_wp * f1 ) q(6,4) = 88.0_wp * ( -91337851897923397.0_wp + & 19696768305507.0_wp * f0 ) / f1 q(7,4) = 242.0_wp * ( -120683.0_wp + 15.0_wp * f0 ) / f3 q(1,5) = 264.0_wp * ( -120683.0_wp + 15.0_wp * f0 ) / f3 q(2,5) = ( -43118111.0_wp + 23357.0_wp * f0 ) / ( 3.0_wp * f3 ) q(3,5) = -47.0_wp * ( -28770085.0_wp + 2259.0_wp * f0 ) / ( 2.0_wp * f3 ) q(4,5) = -3.0_wp * ( 1003619433.0_wp + 11777.0_wp * f0 ) / f3 q(5,5) = -11.0_wp * ( -384168269.0_wp + 65747.0_wp * f0 ) / ( 6.0_wp * f3 ) q(6,5) = 22.0_wp * ( 87290207.0_wp + 10221.0_wp * f0 ) / f3 q(7,5) = -66.0_wp * ( 3692405.0_wp + 419.0_wp * f0 ) / f3 first = .false. end if idel = 1.0_wp / delta if (gsize < 1) call CCTK_WARN (0, "not enough ghostzones") direction: select case (dir) case (0) direction if ( bb(1) == 0 ) then il = 1 + gsize else dvar(1,:,:) = ( q(1,1) * var(1,:,:) + q(2,1) * var(2,:,:) + & q(3,1) * var(3,:,:) + q(4,1) * var(4,:,:) ) * idel dvar(2,:,:) = ( q(1,2) * var(1,:,:) + q(2,2) * var(2,:,:) + & q(3,2) * var(3,:,:) + q(4,2) * var(4,:,:) + & q(5,2) * var(5,:,:) + q(6,2) * var(6,:,:) ) * idel dvar(3,:,:) = ( q(1,3) * var(1,:,:) + q(2,3) * var(2,:,:) + & q(3,3) * var(3,:,:) + q(4,3) * var(4,:,:) + & q(5,3) * var(5,:,:) + q(6,3) * var(6,:,:) ) * idel dvar(4,:,:) = ( q(1,4) * var(1,:,:) + q(2,4) * var(2,:,:) + & q(3,4) * var(3,:,:) + q(4,4) * var(4,:,:) + & q(5,4) * var(5,:,:) + q(6,4) * var(6,:,:) + & q(7,4) * var(7,:,:) ) * idel dvar(5,:,:) = ( q(1,5) * var(1,:,:) + q(2,5) * var(2,:,:) + & q(3,5) * var(3,:,:) + q(4,5) * var(4,:,:) + & q(5,5) * var(5,:,:) + q(6,5) * var(6,:,:) + & q(7,5) * var(7,:,:) ) * idel il = 6 end if if ( bb(2) == 0 ) then ir = ni - gsize else dvar(ni-4,:,:) = - ( q(1,5) * var(ni,:,:) + q(2,5) * var(ni-1,:,:) + & q(3,5) * var(ni-2,:,:) + q(4,5) * var(ni-3,:,:) + & q(5,5) * var(ni-4,:,:) + q(6,5) * var(ni-5,:,:) + & q(7,5) * var(ni-6,:,:) ) * idel dvar(ni-3,:,:) = - ( q(1,4) * var(ni,:,:) + q(2,4) * var(ni-1,:,:) + & q(3,4) * var(ni-2,:,:) + q(4,4) * var(ni-3,:,:) + & q(5,4) * var(ni-4,:,:) + q(6,4) * var(ni-5,:,:) + & q(7,4) * var(ni-6,:,:) ) * idel dvar(ni-2,:,:) = - ( q(1,3) * var(ni,:,:) + q(2,3) * var(ni-1,:,:) + & q(3,3) * var(ni-2,:,:) + q(4,3) * var(ni-3,:,:) + & q(5,3) * var(ni-4,:,:) + & q(6,3) * var(ni-5,:,:) ) * idel dvar(ni-1,:,:) = - ( q(1,2) * var(ni,:,:) + q(2,2) * var(ni-1,:,:) + & q(3,2) * var(ni-2,:,:) + q(4,2) * var(ni-3,:,:) + & q(5,2) * var(ni-4,:,:) + & q(6,2) * var(ni-5,:,:) ) * idel dvar(ni,:,:) = - ( q(1,1) * var(ni,:,:) + q(2,1) * var(ni-1,:,:) + & q(3,1) * var(ni-2,:,:) + & q(4,1) * var(ni-3,:,:) ) * idel ir = ni - 5 end if if (il > ir+1) call CCTK_WARN (0, "domain too small") dvar(il:ir,:,:) = ( a(1) * ( var(il+1:ir+1,:,:) - & var(il-1:ir-1,:,:) ) + & a(2) * ( var(il+2:ir+2,:,:) - & var(il-2:ir-2,:,:) ) ) * idel case (1) direction if ( zero_derivs_y /= 0 ) then dvar = zero else if ( bb(1) == 0 ) then jl = 1 + gsize else dvar(:,1,:) = ( q(1,1) * var(:,1,:) + q(2,1) * var(:,2,:) + & q(3,1) * var(:,3,:) + q(4,1) * var(:,4,:) ) * idel dvar(:,2,:) = ( q(1,2) * var(:,1,:) + q(2,2) * var(:,2,:) + & q(3,2) * var(:,3,:) + q(4,2) * var(:,4,:) + & q(5,2) * var(:,5,:) + q(6,2) * var(:,6,:) ) * idel dvar(:,3,:) = ( q(1,3) * var(:,1,:) + q(2,3) * var(:,2,:) + & q(3,3) * var(:,3,:) + q(4,3) * var(:,4,:) + & q(5,3) * var(:,5,:) + q(6,3) * var(:,6,:) ) * idel dvar(:,4,:) = ( q(1,4) * var(:,1,:) + q(2,4) * var(:,2,:) + & q(3,4) * var(:,3,:) + q(4,4) * var(:,4,:) + & q(5,4) * var(:,5,:) + q(6,4) * var(:,6,:) + & q(7,4) * var(:,7,:) ) * idel dvar(:,5,:) = ( q(1,5) * var(:,1,:) + q(2,5) * var(:,2,:) + & q(3,5) * var(:,3,:) + q(4,5) * var(:,4,:) + & q(5,5) * var(:,5,:) + q(6,5) * var(:,6,:) + & q(7,5) * var(:,7,:) ) * idel jl = 6 end if if ( bb(2) == 0 ) then jr = nj - gsize else dvar(:,nj-4,:) = - ( q(1,5) * var(:,nj,:) + q(2,5) * var(:,nj-1,:) + & q(3,5) * var(:,nj-2,:) + q(4,5) * var(:,nj-3,:) + & q(5,5) * var(:,nj-4,:) + q(6,5) * var(:,nj-5,:) + & q(7,5) * var(:,nj-6,:) ) * idel dvar(:,nj-3,:) = - ( q(1,4) * var(:,nj,:) + q(2,4) * var(:,nj-1,:) + & q(3,4) * var(:,nj-2,:) + q(4,4) * var(:,nj-3,:) + & q(5,4) * var(:,nj-4,:) + q(6,4) * var(:,nj-5,:) + & q(7,4) * var(:,nj-6,:) ) * idel dvar(:,nj-2,:) = - ( q(1,3) * var(:,nj,:) + q(2,3) * var(:,nj-1,:) + & q(3,3) * var(:,nj-2,:) + q(4,3) * var(:,nj-3,:) + & q(5,3) * var(:,nj-4,:) + & q(6,3) * var(:,nj-5,:) ) * idel dvar(:,nj-1,:) = - ( q(1,2) * var(:,nj,:) + q(2,2) * var(:,nj-1,:) + & q(3,2) * var(:,nj-2,:) + q(4,2) * var(:,nj-3,:) + & q(5,2) * var(:,nj-4,:) + & q(6,2) * var(:,nj-5,:) ) * idel dvar(:,nj,:) = - ( q(1,1) * var(:,nj,:) + q(2,1) * var(:,nj-1,:) + & q(3,1) * var(:,nj-2,:) + & q(4,1) * var(:,nj-3,:) ) * idel jr = nj - 5 end if if (jl > jr+1) call CCTK_WARN (0, "domain too small") dvar(:,jl:jr,:) = ( a(1) * ( var(:,jl+1:jr+1,:) - & var(:,jl-1:jr-1,:) ) + & a(2) * ( var(:,jl+2:jr+2,:) - & var(:,jl-2:jr-2,:) ) ) * idel end if case (2) direction if ( zero_derivs_z /= 0 ) then dvar = zero else if ( bb(1) == 0 ) then kl = 1 + gsize else dvar(:,:,1) = ( q(1,1) * var(:,:,1) + q(2,1) * var(:,:,2) + & q(3,1) * var(:,:,3) + q(4,1) * var(:,:,4) ) * idel dvar(:,:,2) = ( q(1,2) * var(:,:,1) + q(2,2) * var(:,:,2) + & q(3,2) * var(:,:,3) + q(4,2) * var(:,:,4) + & q(5,2) * var(:,:,5) + q(6,2) * var(:,:,6) ) * idel dvar(:,:,3) = ( q(1,3) * var(:,:,1) + q(2,3) * var(:,:,2) + & q(3,3) * var(:,:,3) + q(4,3) * var(:,:,4) + & q(5,3) * var(:,:,5) + q(6,3) * var(:,:,6) ) * idel dvar(:,:,4) = ( q(1,4) * var(:,:,1) + q(2,4) * var(:,:,2) + & q(3,4) * var(:,:,3) + q(4,4) * var(:,:,4) + & q(5,4) * var(:,:,5) + q(6,4) * var(:,:,6) + & q(7,4) * var(:,:,7) ) * idel dvar(:,:,5) = ( q(1,5) * var(:,:,1) + q(2,5) * var(:,:,2) + & q(3,5) * var(:,:,3) + q(4,5) * var(:,:,4) + & q(5,5) * var(:,:,5) + q(6,5) * var(:,:,6) + & q(7,5) * var(:,:,7) ) * idel kl = 6 end if if ( bb(2) == 0 ) then kr = nk - gsize else dvar(:,:,nk-4) = - ( q(1,5) * var(:,:,nk) + q(2,5) * var(:,:,nk-1) + & q(3,5) * var(:,:,nk-2) + q(4,5) * var(:,:,nk-3) + & q(5,5) * var(:,:,nk-4) + q(6,5) * var(:,:,nk-5) + & q(7,5) * var(:,:,nk-6) ) * idel dvar(:,:,nk-3) = - ( q(1,4) * var(:,:,nk) + q(2,4) * var(:,:,nk-1) + & q(3,4) * var(:,:,nk-2) + q(4,4) * var(:,:,nk-3) + & q(5,4) * var(:,:,nk-4) + q(6,4) * var(:,:,nk-5) + & q(7,4) * var(:,:,nk-6) ) * idel dvar(:,:,nk-2) = - ( q(1,3) * var(:,:,nk) + q(2,3) * var(:,:,nk-1) + & q(3,3) * var(:,:,nk-2) + q(4,3) * var(:,:,nk-3) + & q(5,3) * var(:,:,nk-4) + & q(6,3) * var(:,:,nk-5) ) * idel dvar(:,:,nk-1) = - ( q(1,2) * var(:,:,nk) + q(2,2) * var(:,:,nk-1) + & q(3,2) * var(:,:,nk-2) + q(4,2) * var(:,:,nk-3) + & q(5,2) * var(:,:,nk-4) + & q(6,2) * var(:,:,nk-5) ) * idel dvar(:,:,nk) = - ( q(1,1) * var(:,:,nk) + q(2,1) * var(:,:,nk-1) + & q(3,1) * var(:,:,nk-2) + & q(4,1) * var(:,:,nk-3) ) * idel kr = nk - 5 end if if (kl > kr+1) call CCTK_WARN (0, "domain too small") dvar(:,:,kl:kr) = ( a(1) * ( var(:,:,kl+1:kr+1) - & var(:,:,kl-1:kr-1) ) + & a(2) * ( var(:,:,kl+2:kr+2) - & var(:,:,kl-2:kr-2) ) ) * idel end if end select direction end subroutine deriv_gf_4_3