1 | |
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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 | ! OSCL1D.f90: "oscillation-indicators" for WENO interp. |
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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 | pure subroutine oscli (npos,nvar,ndof,delx,& |
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39 | & fdat,oscl,dmin) |
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40 | |
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41 | ! |
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42 | ! NPOS no. edges over grid. |
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43 | ! NVAR no. state variables. |
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44 | ! NDOF no. degrees-of-freedom per grid-cell . |
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45 | ! DELX (constant) grid-cell spacing. LENGTH(DELX)==+1 . |
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46 | ! FDAT grid-cell moments array. FDAT is an array with |
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47 | ! SIZE = NDOF-by-NVAR-by-NPOS-1 . |
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48 | ! OSCL grid-cell oscil. dof.'s. OSCL is an array with |
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49 | ! SIZE = +2 -by-NVAR-by-NPOS-1 . |
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50 | ! DMIN min. grid-cell spacing thresh . |
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51 | ! |
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52 | |
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53 | implicit none |
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54 | |
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55 | !------------------------------------------- arguments ! |
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56 | integer, intent( in) :: npos,nvar,ndof |
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57 | real*8 , intent( in) :: dmin |
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58 | real*8 , intent( in) :: delx(:) |
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59 | real*8 , intent( in) :: fdat(:,:,:) |
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60 | real*8 , intent(out) :: oscl(:,:,:) |
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61 | |
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62 | !------------------------------------------- variables ! |
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63 | integer :: ivar,ipos |
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64 | |
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65 | if (npos.lt.3) then |
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66 | !------------------------------- at least 3 grid-cells ! |
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67 | do ipos = +1, npos-1 |
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68 | do ivar = +1, nvar-0 |
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69 | oscl(1,ivar,ipos) = +0.d0 |
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70 | oscl(2,ivar,ipos) = +0.d0 |
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71 | end do |
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72 | end do |
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73 | end if |
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74 | |
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75 | if (npos.lt.3) return |
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76 | if (nvar.lt.1) return |
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77 | if (ndof.lt.1) return |
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78 | |
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79 | if (size(delx).gt.+1) then |
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80 | |
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81 | !------------------------------- variable grid-spacing ! |
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82 | |
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83 | call osclv(npos,nvar,ndof,delx, & |
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84 | & fdat,oscl,dmin) |
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85 | |
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86 | else |
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87 | |
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88 | !------------------------------- constant grid-spacing ! |
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89 | |
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90 | call osclc(npos,nvar,ndof,delx, & |
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91 | & fdat,oscl,dmin) |
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92 | |
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93 | end if |
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94 | |
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95 | return |
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96 | |
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97 | end subroutine |
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98 | |
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99 | pure subroutine osclv (npos,nvar,ndof,delx,& |
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100 | & fdat,oscl,dmin) |
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101 | |
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102 | ! |
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103 | ! *this is the variable grid-spacing variant . |
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104 | ! |
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105 | ! NPOS no. edges over grid. |
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106 | ! NVAR no. state variables. |
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107 | ! NDOF no. degrees-of-freedom per grid-cell . |
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108 | ! DELX (variable) grid-cell spacing. LENGTH(DELX)!=+1 . |
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109 | ! FDAT grid-cell moments array. FDAT is an array with |
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110 | ! SIZE = NDOF-by-NVAR-by-NPOS-1 . |
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111 | ! OSCL grid-cell oscil. dof.'s. OSCL is an array with |
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112 | ! SIZE = +2 -by-NVAR-by-NPOS-1 . |
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113 | ! DMIN min. grid-cell spacing thresh . |
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114 | ! |
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115 | |
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116 | implicit none |
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117 | |
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118 | !------------------------------------------- arguments ! |
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119 | integer, intent( in) :: npos,nvar,ndof |
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120 | real*8 , intent( in) :: dmin |
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121 | real*8 , intent( in) :: delx(:) |
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122 | real*8 , intent( in) :: fdat(:,:,:) |
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123 | real*8 , intent(out) :: oscl(:,:,:) |
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124 | |
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125 | !------------------------------------------- variables ! |
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126 | integer :: head,tail |
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127 | integer :: ipos,ivar |
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128 | real*8 :: hhll,hhcc,hhrr |
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129 | real*8 :: hhmm,hhrc,hhlc |
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130 | real*8 :: cmat(2,3) |
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131 | |
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132 | head = +1 ; tail = npos-1 |
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133 | |
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134 | !--------------------------------------- centred point ! |
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135 | |
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136 | do ipos = head+1, tail-1 |
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137 | |
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138 | hhll = max(delx(ipos-1),dmin) |
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139 | hhcc = max(delx(ipos+0),dmin) |
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140 | hhrr = max(delx(ipos+1),dmin) |
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141 | |
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142 | hhrc = hhrr + hhcc |
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143 | hhlc = hhll + hhcc |
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144 | hhmm = hhll + hhcc + hhrr |
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145 | |
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146 | cmat(1,1) = -(hhcc+2.d0*hhrr)/(hhlc*hhmm) |
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147 | cmat(1,2) = -(hhll-hhrr)* & |
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148 | & (3.d0*hhcc+2.d0*(hhll+hhrr))/& |
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149 | & (hhlc*hhrc*hhmm) |
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150 | cmat(1,3) = +(hhcc+2.d0*hhll)/(hhrc*hhmm) |
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151 | |
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152 | cmat(2,1) = +3.d0/(hhlc*hhmm) |
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153 | cmat(2,2) = -3.d0*(2.d0*hhcc+hhll+hhrr)/& |
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154 | & (hhlc*hhrc*hhmm) |
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155 | cmat(2,3) = +3.d0/(hhrc*hhmm) |
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156 | |
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157 | do ivar = 1, nvar |
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158 | |
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159 | oscl(1,ivar,ipos) = +1.d0 * ( & |
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160 | & + cmat(1,1)*fdat(1,ivar,ipos-1) & |
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161 | & + cmat(1,2)*fdat(1,ivar,ipos+0) & |
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162 | & + cmat(1,3)*fdat(1,ivar,ipos+1) ) |
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163 | |
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164 | oscl(2,ivar,ipos) = +2.d0 * ( & |
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165 | & + cmat(2,1)*fdat(1,ivar,ipos-1) & |
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166 | & + cmat(2,2)*fdat(1,ivar,ipos+0) & |
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167 | & + cmat(2,3)*fdat(1,ivar,ipos+1) ) |
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168 | |
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169 | end do |
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170 | |
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171 | end do |
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172 | |
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173 | !-------------------------------------- lower endpoint ! |
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174 | |
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175 | hhll = max(delx(head+0),dmin) |
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176 | hhcc = max(delx(head+1),dmin) |
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177 | hhrr = max(delx(head+2),dmin) |
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178 | |
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179 | cmat(1,1) = -2.d0 / (hhll+hhcc) |
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180 | cmat(1,2) = +2.d0 / (hhll+hhcc) |
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181 | |
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182 | do ivar = 1, nvar |
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183 | |
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184 | oscl(1,ivar,head) = & |
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185 | & + cmat(1,1)*fdat(1,ivar,head+0) & |
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186 | & + cmat(1,2)*fdat(1,ivar,head+1) |
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187 | |
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188 | oscl(2,ivar,head) = +0.d0 |
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189 | |
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190 | end do |
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191 | |
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192 | !-------------------------------------- upper endpoint ! |
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193 | |
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194 | hhll = max(delx(tail-2),dmin) |
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195 | hhcc = max(delx(tail-1),dmin) |
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196 | hhrr = max(delx(tail-0),dmin) |
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197 | |
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198 | cmat(1,2) = -2.d0 / (hhrr+hhcc) |
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199 | cmat(1,3) = +2.d0 / (hhrr+hhcc) |
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200 | |
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201 | do ivar = 1, nvar |
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202 | |
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203 | oscl(1,ivar,tail) = & |
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204 | & + cmat(1,2)*fdat(1,ivar,tail-1) & |
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205 | & + cmat(1,3)*fdat(1,ivar,tail+0) |
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206 | |
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207 | oscl(2,ivar,tail) = +0.d0 |
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208 | |
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209 | end do |
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210 | |
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211 | return |
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212 | |
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213 | end subroutine |
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214 | |
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215 | pure subroutine osclc (npos,nvar,ndof,delx,& |
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216 | & fdat,oscl,dmin) |
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217 | |
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218 | ! |
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219 | ! *this is the constant grid-spacing variant . |
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220 | ! |
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221 | ! NPOS no. edges over grid. |
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222 | ! NVAR no. state variables. |
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223 | ! NDOF no. degrees-of-freedom per grid-cell . |
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224 | ! DELX (constant) grid-cell spacing. LENGTH(DELX)==+1 . |
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225 | ! FDAT grid-cell moments array. FDAT is an array with |
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226 | ! SIZE = NDOF-by-NVAR-by-NPOS-1 . |
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227 | ! OSCL grid-cell oscil. dof.'s. OSCL is an array with |
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228 | ! SIZE = +2 -by-NVAR-by-NPOS-1 . |
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229 | ! DMIN min. grid-cell spacing thresh . |
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230 | ! |
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231 | |
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232 | implicit none |
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233 | |
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234 | !------------------------------------------- arguments ! |
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235 | integer, intent( in) :: npos,nvar,ndof |
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236 | real*8 , intent( in) :: dmin |
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237 | real*8 , intent( in) :: delx(1) |
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238 | real*8 , intent( in) :: fdat(:,:,:) |
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239 | real*8 , intent(out) :: oscl(:,:,:) |
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240 | |
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241 | !------------------------------------------- variables ! |
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242 | integer :: head,tail,ipos,ivar |
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243 | |
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244 | head = +1; tail = npos - 1 |
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245 | |
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246 | !-------------------------------------- centred points ! |
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247 | |
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248 | do ipos = 2, npos-2 |
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249 | do ivar = 1, nvar-0 |
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250 | |
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251 | oscl(1,ivar,ipos) = & |
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252 | & + .25d+0 * fdat(1,ivar,ipos+1) & |
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253 | & - .25d+0 * fdat(1,ivar,ipos-1) |
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254 | |
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255 | oscl(2,ivar,ipos) = & |
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256 | & + .25d+0 * fdat(1,ivar,ipos+1) & |
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257 | & - .50d+0 * fdat(1,ivar,ipos+0) & |
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258 | & + .25d+0 * fdat(1,ivar,ipos-1) |
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259 | |
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260 | end do |
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261 | end do |
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262 | |
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263 | !-------------------------------------- lower endpoint ! |
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264 | |
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265 | do ivar = 1, nvar |
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266 | |
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267 | oscl(1,ivar,head) = & |
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268 | & + .50d+0 * fdat(1,ivar,head+1) & |
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269 | & - .50d+0 * fdat(1,ivar,head+0) |
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270 | |
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271 | oscl(2,ivar,head) = +0.d0 |
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272 | |
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273 | end do |
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274 | |
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275 | !-------------------------------------- upper endpoint ! |
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276 | |
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277 | do ivar = 1, nvar |
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278 | |
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279 | oscl(1,ivar,tail) = & |
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280 | & + .50d+0 * fdat(1,ivar,tail+0) & |
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281 | & - .50d+0 * fdat(1,ivar,tail-1) |
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282 | |
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283 | oscl(2,ivar,tail) = +0.d0 |
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284 | |
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285 | end do |
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286 | |
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287 | return |
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288 | |
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289 | end subroutine |
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290 | |
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291 | |
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292 | |
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