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2 | ! gfortran -cpp -O3 -flto ex_5.f90 -o ex_5 |
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3 | ! ./ex_5 |
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4 | |
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5 | ! Assemble high-order interpolants over a uniform domain. |
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6 | ! |
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7 | |
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8 | # include "../src/ppr_1d.f90" |
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9 | |
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10 | program ex |
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11 | |
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12 | use ppr_1d |
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13 | |
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14 | implicit none |
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15 | |
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16 | integer, parameter :: npos = 43 ! no. edge |
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17 | integer, parameter :: nvar = 1 ! no. variables to build |
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18 | integer, parameter :: ndof = 1 ! no. FV DoF per cell |
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19 | integer :: ipos,jpos,mdof |
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20 | |
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21 | !------------------------------- domain discretisation ! |
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22 | real*8 :: xpos(npos),xdel(1) |
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23 | real*8 :: xmid,xhat,xloc,floc |
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24 | |
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25 | !-------------------------------- finite-volume arrays ! |
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26 | |
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27 | ! Arrays represent a "block" of finite-volume tracers |
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28 | ! to remap. The 1st dim. is the no. of DoF per cell, |
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29 | ! NDOF=1 is a standard finite-volume scheme where the |
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30 | ! data is specified as cell means. NDOF>1 is reserved |
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31 | ! for future use with DG-style schemes. NVAR is the |
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32 | ! number of tracers to remap. Processing tracers in a |
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33 | ! batch is typically more efficient than one-by-one. |
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34 | ! The last dim. is the no. cells (layers) in the grid. |
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35 | |
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36 | real*8 :: fdat(ndof,nvar,npos-1) |
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37 | |
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38 | !-------------------------------- reconstruction coeff ! |
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39 | |
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40 | ! Coeff. for the piecewise polynomial reconstruction. |
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41 | ! A polynomial is assembled for each cell w.r.t. a |
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42 | ! "local" cell coordinate system: each cell is mapped |
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43 | ! onto [-1,+1]. The interpolants can be evaluated by |
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44 | ! taking the product FHAT*BVEC, where BVEC is a basis |
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45 | ! vector assembled at the interpolation points. Basis |
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46 | ! vectors can eb assembled via calls to BFUN1D(). |
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47 | |
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48 | real*8 :: fhat( 5,nvar,npos-1) |
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49 | real*8 :: bvec( 5) |
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50 | real*8 :: spos( 5) |
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51 | |
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52 | !------------------------------ method data-structures ! |
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53 | type(rcon_work) :: work |
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54 | type(rcon_opts) :: opts |
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55 | type(rcon_ends) :: bc_l(nvar) |
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56 | type(rcon_ends) :: bc_r(nvar) |
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57 | |
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58 | !------------------------------ define a simple domain ! |
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59 | |
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60 | call linspace(0.d0,1.d0,npos,xpos) |
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61 | |
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62 | xdel(1) = (xpos(npos)& |
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63 | & - xpos( 1)) / (npos- 1) |
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64 | |
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65 | !------------------------------ setup some simple data ! |
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66 | |
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67 | do ipos = +1, npos-1 |
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68 | |
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69 | xmid = xpos(ipos+0) * 0.5d+0 & |
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70 | & + xpos(ipos+1) * 0.5d+0 |
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71 | |
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72 | fdat(1,1,ipos) = & |
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73 | & .8d+0 * exp( -75.0d+0 * (xmid - 0.275d+0) ** 2 ) & |
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74 | & + .9d+0 * exp(-100.0d+0 * (xmid - 0.500d+0) ** 2 ) & |
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75 | & + 1.d+0 * exp(-125.0d+0 * (xmid - 0.725d+0) ** 2 ) |
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76 | |
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77 | end do |
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78 | |
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79 | !------------------------------ specify method options ! |
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80 | |
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81 | opts%edge_meth = p5e_method ! 5th-order edge interp. |
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82 | opts%cell_meth = pqm_method ! PPM method in cells |
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83 | opts%cell_lims = mono_limit ! monotone limiter |
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84 | |
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85 | !------------------------------ set BC.'s at endpoints ! |
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86 | |
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87 | bc_l%bcopt = bcon_loose ! "loose" = extrapolate |
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88 | bc_r%bcopt = bcon_loose |
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89 | |
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90 | !------------------------------ init. method workspace ! |
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91 | |
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92 | call work%init(npos,nvar,opts) |
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93 | |
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94 | !------------------------------ build cell polynomials ! |
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95 | |
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96 | fhat = 0.d+0 |
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97 | |
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98 | mdof = ndof1d (opts%cell_meth) |
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99 | |
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100 | call rcon1d(npos,nvar,ndof,xdel, & |
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101 | & fdat,bc_l,bc_r,fhat, & |
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102 | & work,opts) |
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103 | |
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104 | !------------------------------ clear method workspace ! |
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105 | |
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106 | call work%free() |
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107 | |
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108 | !------------------------------ dump results to stdout ! |
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109 | |
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110 | print*,"Eval. PPR interpolant: " |
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111 | |
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112 | spos(1) = -1.0d+0 ! eval. at local points |
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113 | spos(2) = -0.5d+0 |
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114 | spos(3) = +0.0d+0 |
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115 | spos(4) = +0.5d+0 |
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116 | spos(5) = +1.0d+0 |
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117 | |
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118 | do ipos = +1, npos-1 |
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119 | do jpos = +1, +5 |
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120 | |
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121 | xmid = xpos(ipos+1)* 0.5d+0 & |
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122 | & + xpos(ipos+0)* 0.5d+0 |
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123 | |
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124 | xhat = xpos(ipos+1)* 0.5d+0 & |
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125 | & - xpos(ipos+0)* 0.5d+0 |
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126 | |
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127 | xloc = xmid + spos(jpos)*xhat |
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128 | |
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129 | call bfun1d(0,mdof,spos(jpos),bvec) |
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130 | |
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131 | floc = dot_product( & |
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132 | & fhat(+1:mdof,1,ipos),bvec(+1:mdof)) |
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133 | |
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134 | print *, xloc, floc |
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135 | |
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136 | end do |
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137 | end do |
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138 | |
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139 | end program |
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140 | |
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141 | |
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142 | |
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