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| 2 | ! |
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| 3 | ! This program may be freely redistributed under the |
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| 4 | ! condition that the copyright notices (including this |
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| 5 | ! entire header) are not removed, and no compensation |
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| 6 | ! is received through use of the software. Private, |
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| 7 | ! research, and institutional use is free. You may |
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| 8 | ! distribute modified versions of this code UNDER THE |
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| 9 | ! CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE |
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| 10 | ! TO IT IN THE SAME FILE REMAIN UNDER COPYRIGHT OF THE |
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| 11 | ! ORIGINAL AUTHOR, BOTH SOURCE AND OBJECT CODE ARE |
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| 12 | ! MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR |
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| 13 | ! NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution |
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| 14 | ! of this code as part of a commercial system is |
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| 15 | ! permissible ONLY BY DIRECT ARRANGEMENT WITH THE |
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| 16 | ! AUTHOR. (If you are not directly supplying this |
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| 17 | ! code to a customer, and you are instead telling them |
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| 18 | ! how they can obtain it for free, then you are not |
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| 19 | ! required to make any arrangement with me.) |
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| 20 | ! |
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| 21 | ! Disclaimer: Neither I nor: Columbia University, the |
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| 22 | ! National Aeronautics and Space Administration, nor |
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| 23 | ! the Massachusetts Institute of Technology warrant |
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| 24 | ! or certify this code in any way whatsoever. This |
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| 25 | ! code is provided "as-is" to be used at your own risk. |
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| 26 | ! |
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| 27 | ! |
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| 28 | |
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| 29 | ! |
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| 30 | ! PPM.h90: 1d slope-limited, piecewise parabolic recon. |
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| 31 | ! |
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| 32 | ! Darren Engwirda |
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| 33 | ! 08-Sep-2016 |
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| 34 | ! de2363 [at] columbia [dot] edu |
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| 35 | ! |
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| 36 | ! |
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| 37 | |
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| 38 | ! P. Colella and PR. Woodward, The Piecewise Parabolic |
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| 39 | ! Method (PPM) for gas-dynamical simulations., J. Comp. |
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| 40 | ! Phys., 54 (1), 1984, 174-201, |
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| 41 | ! https://doi.org/10.1016/0021-9991(84)90143-8 |
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| 42 | ! |
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| 43 | |
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| 44 | pure subroutine ppm(npos,nvar,ndof,delx, & |
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| 45 | & fdat,fhat,edge,oscl, & |
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| 46 | & dmin,ilim,wlim,halo) |
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| 47 | |
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| 48 | ! |
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| 49 | ! NPOS no. edges over grid. |
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| 50 | ! NVAR no. state variables. |
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| 51 | ! NDOF no. degrees-of-freedom per grid-cell. |
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| 52 | ! DELX grid-cell spacing array. LENGTH(DELX) == +1 if |
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| 53 | ! spacing is uniform . |
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| 54 | ! FDAT grid-cell moments array. FDAT is an array with |
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| 55 | ! SIZE = NDOF-by-NVAR-by-NPOS-1 . |
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| 56 | ! FHAT grid-cell re-con. array. FHAT is an array with |
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| 57 | ! SIZE = MDOF-by-NVAR-by-NPOS-1 . |
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| 58 | ! EDGE edge-centred interp. for function-value. EDGE |
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| 59 | ! is an array with SIZE = NVAR-by-NPOS . |
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| 60 | ! OSCL grid-cell oscil. dof.'s. OSCL is an array with |
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| 61 | ! SIZE = +2 -by-NVAR-by-NPOS-1 . |
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| 62 | ! DMIN min. grid-cell spacing thresh . |
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| 63 | ! ILIM cell slope-limiting selection . |
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| 64 | ! WLIM wall slope-limiting selection . |
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| 65 | ! HALO width of re-con. stencil, symmetric about mid. . |
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| 66 | ! |
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| 67 | |
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| 68 | implicit none |
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| 69 | |
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| 70 | !------------------------------------------- arguments ! |
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| 71 | integer, intent(in) :: npos,nvar,ndof |
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| 72 | real*8 , intent(in) :: dmin |
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| 73 | real*8 , intent(out) :: fhat(:,:,:) |
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| 74 | real*8 , intent(in) :: oscl(:,:,:) |
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| 75 | real*8 , intent(in) :: delx(:) |
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| 76 | real*8 , intent(in) :: fdat(:,:,:) |
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| 77 | real*8 , intent(in) :: edge(:,:) |
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| 78 | integer, intent(in) :: ilim,wlim,halo |
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| 79 | |
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| 80 | !------------------------------------------- variables ! |
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| 81 | integer :: ipos,ivar,iill,iirr,head,tail |
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| 82 | real*8 :: ff00,ffll,ffrr,hh00,hhll,hhrr |
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| 83 | integer :: mono |
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| 84 | real*8 :: fell,ferr |
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| 85 | real*8 :: dfds(-1:+1) |
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| 86 | real*8 :: wval(+1:+2) |
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| 87 | real*8 :: uhat(+1:+3) |
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| 88 | real*8 :: lhat(+1:+3) |
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| 89 | |
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| 90 | head = +1; tail = npos - 1 |
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| 91 | |
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| 92 | if (npos.eq.2) then |
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| 93 | !----- default to reduced order if insufficient points ! |
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| 94 | do ivar = +1, nvar |
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| 95 | fhat(1,ivar,+1) = & |
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| 96 | & fdat(1,ivar,+1) |
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| 97 | fhat(2,ivar,+1) = 0.d0 |
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| 98 | fhat(3,ivar,+1) = 0.d0 |
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| 99 | end do |
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| 100 | end if |
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| 101 | |
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| 102 | if (npos.le.2) return |
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| 103 | |
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| 104 | !------------------- reconstruct function on each cell ! |
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| 105 | |
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| 106 | uhat = +0.d+0 |
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| 107 | lhat = +0.d+0 |
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| 108 | |
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| 109 | do ipos = +1 , npos-1 |
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| 110 | |
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| 111 | iill = max(head,ipos-1) |
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| 112 | iirr = min(tail,ipos+1) |
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| 113 | |
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| 114 | do ivar = +1 , nvar-0 |
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| 115 | |
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| 116 | !----------------------------- cell mean + edge values ! |
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| 117 | |
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| 118 | ff00 = fdat(1,ivar,ipos) |
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| 119 | ffll = fdat(1,ivar,iill) |
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| 120 | ffrr = fdat(1,ivar,iirr) |
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| 121 | |
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| 122 | fell = edge(ivar,ipos+0) |
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| 123 | ferr = edge(ivar,ipos+1) |
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| 124 | |
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| 125 | !----------------------------- calc. LL/00/RR gradient ! |
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| 126 | |
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| 127 | if (size(delx).gt.+1) then |
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| 128 | |
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| 129 | hh00 = delx(ipos) |
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| 130 | hhll = delx(iill) |
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| 131 | hhrr = delx(iirr) |
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| 132 | |
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| 133 | call plsv (ffll,hhll,ff00, & |
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| 134 | & hh00,ffrr,hhrr, & |
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| 135 | & dfds) |
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| 136 | else |
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| 137 | |
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| 138 | call plsc (ffll,ff00,ffrr, & |
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| 139 | & dfds) |
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| 140 | |
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| 141 | end if |
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| 142 | |
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| 143 | !----------------------------- calc. cell-wise profile ! |
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| 144 | |
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| 145 | select case(ilim) |
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| 146 | case (null_limit) |
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| 147 | |
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| 148 | !----------------------------- calc. unlimited profile ! |
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| 149 | |
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| 150 | call ppmfn(ff00,ffll,ffrr, & |
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| 151 | & fell,ferr,dfds, & |
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| 152 | & uhat,lhat,mono) |
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| 153 | |
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| 154 | !----------------------------- pref. unlimited profile ! |
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| 155 | |
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| 156 | wval(1) = +1.d+0 |
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| 157 | wval(2) = +0.d+0 |
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| 158 | |
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| 159 | case (mono_limit) |
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| 160 | |
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| 161 | !----------------------------- calc. monotonic profile ! |
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| 162 | |
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| 163 | call ppmfn(ff00,ffll,ffrr, & |
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| 164 | & fell,ferr,dfds, & |
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| 165 | & uhat,lhat,mono) |
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| 166 | |
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| 167 | !----------------------------- pref. monotonic profile ! |
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| 168 | |
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| 169 | wval(1) = +0.d+0 |
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| 170 | wval(2) = +1.d+0 |
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| 171 | |
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| 172 | case (weno_limit) |
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| 173 | |
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| 174 | !----------------------------- calc. unlimited profile ! |
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| 175 | |
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| 176 | call ppmfn(ff00,ffll,ffrr, & |
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| 177 | & fell,ferr,dfds, & |
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| 178 | & uhat,lhat,mono) |
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| 179 | |
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| 180 | if (mono.gt.+0) then |
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| 181 | |
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| 182 | !----------------------------- calc. WENO-type weights ! |
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| 183 | |
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| 184 | call wenoi(npos,delx,oscl, & |
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| 185 | & ipos,ivar,halo, & |
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| 186 | & wlim,wval) |
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| 187 | |
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| 188 | else |
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| 189 | |
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| 190 | !----------------------------- pref. unlimited profile ! |
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| 191 | |
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| 192 | wval(1) = +1.d+0 |
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| 193 | wval(2) = +0.d+0 |
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| 194 | |
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| 195 | end if |
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| 196 | |
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| 197 | end select |
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| 198 | |
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| 199 | !----------------------------- blend "null" and "mono" ! |
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| 200 | |
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| 201 | fhat(1,ivar,ipos) = & |
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| 202 | & wval(1) * uhat(1) + & |
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| 203 | & wval(2) * lhat(1) |
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| 204 | fhat(2,ivar,ipos) = & |
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| 205 | & wval(1) * uhat(2) + & |
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| 206 | & wval(2) * lhat(2) |
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| 207 | fhat(3,ivar,ipos) = & |
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| 208 | & wval(1) * uhat(3) + & |
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| 209 | & wval(2) * lhat(3) |
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| 210 | |
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| 211 | end do |
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| 212 | |
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| 213 | end do |
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| 214 | |
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| 215 | return |
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| 216 | |
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| 217 | end subroutine |
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| 218 | |
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| 219 | !--------- assemble piecewise parabolic reconstruction ! |
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| 220 | |
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| 221 | pure subroutine ppmfn(ff00,ffll,ffrr,fell,& |
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| 222 | & ferr,dfds,uhat,lhat,& |
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| 223 | & mono) |
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| 224 | |
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| 225 | ! |
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| 226 | ! FF00 centred grid-cell mean. |
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| 227 | ! FFLL left -biased grid-cell mean. |
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| 228 | ! FFRR right-biased grid-cell mean. |
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| 229 | ! FELL left -biased edge interp. |
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| 230 | ! FERR right-biased edge interp. |
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| 231 | ! DFDS piecewise linear gradients in local co-ord.'s. |
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| 232 | ! DFDS(+0) is a centred, slope-limited estimate, |
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| 233 | ! DFDS(-1), DFDS(+1) are left- and right-biased |
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| 234 | ! estimates (unlimited). |
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| 235 | ! UHAT unlimited PPM reconstruction coefficients . |
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| 236 | ! LHAT monotonic PPM reconstruction coefficients . |
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| 237 | ! MONO slope-limiting indicator, MONO > +0 if some |
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| 238 | ! limiting has occured . |
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| 239 | ! |
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| 240 | |
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| 241 | implicit none |
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| 242 | |
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| 243 | !------------------------------------------- arguments ! |
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| 244 | real*8 , intent(in) :: ff00 |
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| 245 | real*8 , intent(in) :: ffll,ffrr |
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| 246 | real*8 , intent(inout) :: fell,ferr |
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| 247 | real*8 , intent(in) :: dfds(-1:+1) |
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| 248 | real*8 , intent(out) :: uhat(+1:+3) |
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| 249 | real*8 , intent(out) :: lhat(+1:+3) |
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| 250 | integer, intent(out) :: mono |
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| 251 | |
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| 252 | !------------------------------------------- variables ! |
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| 253 | real*8 :: turn |
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| 254 | |
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| 255 | mono = 0 |
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| 256 | |
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| 257 | !-------------------------------- "null" slope-limiter ! |
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| 258 | |
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| 259 | uhat( 1 ) = & |
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| 260 | & + (3.0d+0 / 2.0d+0) * ff00 & |
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| 261 | & - (1.0d+0 / 4.0d+0) *(ferr+fell) |
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| 262 | uhat( 2 ) = & |
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| 263 | & + (1.0d+0 / 2.0d+0) *(ferr-fell) |
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| 264 | uhat( 3 ) = & |
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| 265 | & - (3.0d+0 / 2.0d+0) * ff00 & |
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| 266 | & + (3.0d+0 / 4.0d+0) *(ferr+fell) |
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| 267 | |
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| 268 | !-------------------------------- "mono" slope-limiter ! |
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| 269 | |
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| 270 | if((ffrr - ff00) * & |
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| 271 | & (ff00 - ffll) .lt. 0.d+0) then |
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| 272 | |
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| 273 | !----------------------------------- "flatten" extrema ! |
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| 274 | |
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| 275 | mono = +1 |
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| 276 | |
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| 277 | lhat(1) = ff00 |
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| 278 | lhat(2) = 0.d0 |
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| 279 | lhat(3) = 0.d0 |
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| 280 | |
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| 281 | return |
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| 282 | |
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| 283 | end if |
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| 284 | |
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| 285 | !----------------------------------- limit edge values ! |
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| 286 | |
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| 287 | if((ffll - fell) * & |
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| 288 | & (fell - ff00) .le. 0.d+0) then |
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| 289 | |
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| 290 | mono = +1 |
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| 291 | |
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| 292 | fell = ff00 - dfds(0) |
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| 293 | |
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| 294 | end if |
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| 295 | |
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| 296 | if((ffrr - ferr) * & |
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| 297 | & (ferr - ff00) .le. 0.d+0) then |
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| 298 | |
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| 299 | mono = +1 |
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| 300 | |
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| 301 | ferr = ff00 + dfds(0) |
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| 302 | |
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| 303 | end if |
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| 304 | |
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| 305 | !----------------------------------- update ppm coeff. ! |
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| 306 | |
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| 307 | lhat( 1 ) = & |
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| 308 | & + (3.0d+0 / 2.0d+0) * ff00 & |
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| 309 | & - (1.0d+0 / 4.0d+0) *(ferr+fell) |
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| 310 | lhat( 2 ) = & |
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| 311 | & + (1.0d+0 / 2.0d+0) *(ferr-fell) |
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| 312 | lhat( 3 ) = & |
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| 313 | & - (3.0d+0 / 2.0d+0) * ff00 & |
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| 314 | & + (3.0d+0 / 4.0d+0) *(ferr+fell) |
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| 315 | |
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| 316 | !----------------------------------- limit cell values ! |
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| 317 | |
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| 318 | if (abs(lhat(3)) .gt. & |
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| 319 | & abs(lhat(2))*.5d+0) then |
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| 320 | |
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| 321 | turn = -0.5d+0 * lhat(2) & |
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| 322 | & / lhat(3) |
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| 323 | |
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| 324 | if ((turn .ge. -1.d+0)& |
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| 325 | & .and.(turn .le. +0.d+0)) then |
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| 326 | |
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| 327 | mono = +2 |
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| 328 | |
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| 329 | !--------------------------- push TURN onto lower edge ! |
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| 330 | |
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| 331 | ferr = +3.0d+0 * ff00 & |
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| 332 | & -2.0d+0 * fell |
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| 333 | |
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| 334 | lhat( 1 ) = & |
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| 335 | & + (3.0d+0 / 2.0d+0) * ff00 & |
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| 336 | & - (1.0d+0 / 4.0d+0) *(ferr+fell) |
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| 337 | lhat( 2 ) = & |
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| 338 | & + (1.0d+0 / 2.0d+0) *(ferr-fell) |
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| 339 | lhat( 3 ) = & |
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| 340 | & - (3.0d+0 / 2.0d+0) * ff00 & |
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| 341 | & + (3.0d+0 / 4.0d+0) *(ferr+fell) |
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| 342 | |
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| 343 | else & |
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| 344 | & if ((turn .gt. +0.d+0)& |
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| 345 | & .and.(turn .le. +1.d+0)) then |
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| 346 | |
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| 347 | mono = +2 |
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| 348 | |
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| 349 | !--------------------------- push TURN onto upper edge ! |
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| 350 | |
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| 351 | fell = +3.0d+0 * ff00 & |
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| 352 | & -2.0d+0 * ferr |
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| 353 | |
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| 354 | lhat( 1 ) = & |
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| 355 | & + (3.0d+0 / 2.0d+0) * ff00 & |
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| 356 | & - (1.0d+0 / 4.0d+0) *(ferr+fell) |
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| 357 | lhat( 2 ) = & |
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| 358 | & + (1.0d+0 / 2.0d+0) *(ferr-fell) |
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| 359 | lhat( 3 ) = & |
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| 360 | & - (3.0d+0 / 2.0d+0) * ff00 & |
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| 361 | & + (3.0d+0 / 4.0d+0) *(ferr+fell) |
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| 362 | |
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| 363 | end if |
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| 364 | |
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| 365 | end if |
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| 366 | |
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| 367 | return |
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| 368 | |
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| 369 | end subroutine |
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| 370 | |
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| 371 | |
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| 372 | |
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