| 1 | MODULE slopes_m |
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| 2 | |
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| 3 | ! Author: Lionel GUEZ |
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| 4 | ! Extension / factorisation: David CUGNET |
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| 5 | |
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| 6 | IMPLICIT NONE |
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| 7 | |
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| 8 | ! Those generic function computes second order slopes with Van |
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| 9 | ! Leer slope-limiting, given cell averages. Reference: Dukowicz, |
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| 10 | ! 1987, SIAM Journal on Scientific and Statistical Computing, 8, |
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| 11 | ! 305. |
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| 12 | |
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| 13 | ! The only difference between the specific functions is the rank |
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| 14 | ! of the first argument and the equal rank of the result. |
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| 15 | |
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| 16 | ! slope(ix,...) acts on ix th dimension. |
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| 17 | |
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| 18 | ! real, intent(in), rank >= 1:: f ! (n, ...) cell averages, n must be >= 1 |
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| 19 | ! real, intent(in):: x(:) ! (n + 1) cell edges |
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| 20 | ! real slopes, same shape as f ! (n, ...) |
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| 21 | INTERFACE slopes |
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| 22 | MODULE procedure slopes1, slopes2, slopes3, slopes4, slopes5 |
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| 23 | END INTERFACE |
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| 24 | |
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| 25 | PRIVATE |
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| 26 | PUBLIC :: slopes |
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| 27 | |
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| 28 | CONTAINS |
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| 29 | |
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| 30 | !------------------------------------------------------------------------------- |
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| 31 | ! |
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| 32 | PURE FUNCTION slopes1(ix, f, x) |
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| 33 | ! |
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| 34 | !------------------------------------------------------------------------------- |
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| 35 | ! Arguments: |
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| 36 | INTEGER, INTENT(IN) :: ix |
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| 37 | REAL, INTENT(IN) :: f(:) |
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| 38 | REAL, INTENT(IN) :: x(:) |
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| 39 | REAL :: slopes1(SIZE(f,1)) |
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| 40 | !------------------------------------------------------------------------------- |
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| 41 | ! Local: |
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| 42 | INTEGER :: n, i, j, sta(2), sto(2) |
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| 43 | REAL :: xc(SIZE(f,1)) ! (n) cell centers |
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| 44 | REAL :: h(2:SIZE(f,1)-1), delta_xc(2:SIZE(f,1)-1) ! (2:n-1) |
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| 45 | REAL :: fm, ff, fp, dx |
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| 46 | !------------------------------------------------------------------------------- |
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| 47 | n=SIZE(f,ix) |
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| 48 | FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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| 49 | FORALL(i=2:n-1) |
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| 50 | h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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| 51 | END FORALL |
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| 52 | slopes1(:)=0. |
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| 53 | DO i=2,n-1 |
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| 54 | ff=f(i); fm=f(i-1); fp=f(i+1) |
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| 55 | IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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| 56 | slopes1(i)=0.; CYCLE !--- Local extremum |
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| 57 | !--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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| 58 | slopes1(i)=(fp-fm)/delta_xc(i) |
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| 59 | !--- Slope limitation |
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| 60 | slopes1(i) = SIGN(MIN(ABS(slopes1(i)), & |
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| 61 | ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes1(i) ) |
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| 62 | END IF |
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| 63 | END DO |
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| 64 | |
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| 65 | END FUNCTION slopes1 |
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| 66 | ! |
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| 67 | !------------------------------------------------------------------------------- |
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| 68 | |
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| 69 | |
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| 70 | !------------------------------------------------------------------------------- |
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| 71 | ! |
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| 72 | PURE FUNCTION slopes2(ix, f, x) |
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| 73 | ! |
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| 74 | !------------------------------------------------------------------------------- |
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| 75 | ! Arguments: |
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| 76 | INTEGER, INTENT(IN) :: ix |
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| 77 | REAL, INTENT(IN) :: f(:, :) |
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| 78 | REAL, INTENT(IN) :: x(:) |
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| 79 | REAL :: slopes2(SIZE(f,1),SIZE(f,2)) |
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| 80 | !------------------------------------------------------------------------------- |
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| 81 | ! Local: |
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| 82 | INTEGER :: n, i, j, sta(2), sto(2) |
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| 83 | REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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| 84 | REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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| 85 | REAL :: fm, ff, fp, dx |
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| 86 | !------------------------------------------------------------------------------- |
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| 87 | n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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| 88 | FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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| 89 | FORALL(i=2:n-1) |
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| 90 | h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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| 91 | END FORALL |
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| 92 | slopes2(:,:)=0. |
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| 93 | sta=[1,1]; sta(ix)=2 |
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| 94 | sto=SHAPE(f); sto(ix)=n-1 |
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| 95 | DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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| 96 | DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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| 97 | ff=f(i,j) |
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| 98 | SELECT CASE(ix) |
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| 99 | CASE(1); fm=f(i-1,j); fp=f(i+1,j) |
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| 100 | CASE(2); fm=f(i,j-1); fp=f(i,j+1) |
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| 101 | END SELECT |
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| 102 | IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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| 103 | slopes2(i,j)=0.; CYCLE !--- Local extremum |
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| 104 | !--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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| 105 | slopes2(i,j)=(fp-fm)/dx |
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| 106 | !--- Slope limitation |
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| 107 | slopes2(i,j) = SIGN(MIN(ABS(slopes2(i,j)), & |
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| 108 | ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes2(i,j) ) |
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| 109 | END IF |
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| 110 | END DO |
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| 111 | END DO |
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| 112 | DEALLOCATE(xc,h,delta_xc) |
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| 113 | |
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| 114 | END FUNCTION slopes2 |
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| 115 | ! |
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| 116 | !------------------------------------------------------------------------------- |
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| 117 | |
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| 118 | |
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| 119 | !------------------------------------------------------------------------------- |
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| 120 | ! |
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| 121 | PURE FUNCTION slopes3(ix, f, x) |
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| 122 | ! |
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| 123 | !------------------------------------------------------------------------------- |
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| 124 | ! Arguments: |
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| 125 | INTEGER, INTENT(IN) :: ix |
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| 126 | REAL, INTENT(IN) :: f(:, :, :) |
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| 127 | REAL, INTENT(IN) :: x(:) |
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| 128 | REAL :: slopes3(SIZE(f,1),SIZE(f,2),SIZE(f,3)) |
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| 129 | !------------------------------------------------------------------------------- |
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| 130 | ! Local: |
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| 131 | INTEGER :: n, i, j, k, sta(3), sto(3) |
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| 132 | REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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| 133 | REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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| 134 | REAL :: fm, ff, fp, dx |
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| 135 | !------------------------------------------------------------------------------- |
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| 136 | n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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| 137 | FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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| 138 | FORALL(i=2:n-1) |
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| 139 | h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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| 140 | END FORALL |
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| 141 | slopes3(:,:,:)=0. |
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| 142 | sta=[1,1,1]; sta(ix)=2 |
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| 143 | sto=SHAPE(f); sto(ix)=n-1 |
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| 144 | DO k=sta(3),sto(3); IF(ix==3) dx=delta_xc(k) |
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| 145 | DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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| 146 | DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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| 147 | ff=f(i,j,k) |
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| 148 | SELECT CASE(ix) |
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| 149 | CASE(1); fm=f(i-1,j,k); fp=f(i+1,j,k) |
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| 150 | CASE(2); fm=f(i,j-1,k); fp=f(i,j+1,k) |
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| 151 | CASE(3); fm=f(i,j,k-1); fp=f(i,j,k+1) |
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| 152 | END SELECT |
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| 153 | IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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| 154 | slopes3(i,j,k)=0.; CYCLE !--- Local extremum |
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| 155 | !--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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| 156 | slopes3(i,j,k)=(fp-fm)/dx |
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| 157 | !--- Slope limitation |
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| 158 | slopes3(i,j,k) = SIGN(MIN(ABS(slopes3(i,j,k)), & |
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| 159 | ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes3(i,j,k) ) |
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| 160 | END IF |
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| 161 | END DO |
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| 162 | END DO |
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| 163 | END DO |
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| 164 | DEALLOCATE(xc,h,delta_xc) |
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| 165 | |
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| 166 | END FUNCTION slopes3 |
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| 167 | ! |
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| 168 | !------------------------------------------------------------------------------- |
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| 169 | |
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| 170 | |
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| 171 | !------------------------------------------------------------------------------- |
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| 172 | ! |
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| 173 | PURE FUNCTION slopes4(ix, f, x) |
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| 174 | ! |
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| 175 | !------------------------------------------------------------------------------- |
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| 176 | ! Arguments: |
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| 177 | INTEGER, INTENT(IN) :: ix |
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| 178 | REAL, INTENT(IN) :: f(:, :, :, :) |
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| 179 | REAL, INTENT(IN) :: x(:) |
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| 180 | REAL :: slopes4(SIZE(f,1),SIZE(f,2),SIZE(f,3),SIZE(f,4)) |
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| 181 | !------------------------------------------------------------------------------- |
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| 182 | ! Local: |
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| 183 | INTEGER :: n, i, j, k, l, m, sta(4), sto(4) |
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| 184 | REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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| 185 | REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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| 186 | REAL :: fm, ff, fp, dx |
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| 187 | !------------------------------------------------------------------------------- |
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| 188 | n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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| 189 | FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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| 190 | FORALL(i=2:n-1) |
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| 191 | h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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| 192 | END FORALL |
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| 193 | slopes4(:,:,:,:)=0. |
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| 194 | sta=[1,1,1,1]; sta(ix)=2 |
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| 195 | sto=SHAPE(f); sto(ix)=n-1 |
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| 196 | DO l=sta(4),sto(4); IF(ix==4) dx=delta_xc(l) |
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| 197 | DO k=sta(3),sto(3); IF(ix==3) dx=delta_xc(k) |
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| 198 | DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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| 199 | DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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| 200 | ff=f(i,j,k,l) |
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| 201 | SELECT CASE(ix) |
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| 202 | CASE(1); fm=f(i-1,j,k,l); fp=f(i+1,j,k,l) |
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| 203 | CASE(2); fm=f(i,j-1,k,l); fp=f(i,j+1,k,l) |
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| 204 | CASE(3); fm=f(i,j,k-1,l); fp=f(i,j,k+1,l) |
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| 205 | CASE(4); fm=f(i,j,k,l-1); fp=f(i,j,k,l+1) |
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| 206 | END SELECT |
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| 207 | IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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| 208 | slopes4(i,j,k,l)=0.; CYCLE !--- Local extremum |
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| 209 | !--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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| 210 | slopes4(i,j,k,l)=(fp-fm)/dx |
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| 211 | !--- Slope limitation |
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| 212 | slopes4(i,j,k,l) = SIGN(MIN(ABS(slopes4(i,j,k,l)), & |
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| 213 | ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes4(i,j,k,l) ) |
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| 214 | END IF |
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| 215 | END DO |
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| 216 | END DO |
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| 217 | END DO |
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| 218 | END DO |
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| 219 | DEALLOCATE(xc,h,delta_xc) |
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| 220 | |
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| 221 | END FUNCTION slopes4 |
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| 222 | ! |
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| 223 | !------------------------------------------------------------------------------- |
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| 224 | |
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| 225 | |
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| 226 | !------------------------------------------------------------------------------- |
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| 227 | ! |
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| 228 | PURE FUNCTION slopes5(ix, f, x) |
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| 229 | ! |
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| 230 | !------------------------------------------------------------------------------- |
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| 231 | ! Arguments: |
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| 232 | INTEGER, INTENT(IN) :: ix |
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| 233 | REAL, INTENT(IN) :: f(:, :, :, :, :) |
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| 234 | REAL, INTENT(IN) :: x(:) |
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| 235 | REAL :: slopes5(SIZE(f,1),SIZE(f,2),SIZE(f,3),SIZE(f,4),SIZE(f,5)) |
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| 236 | !------------------------------------------------------------------------------- |
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| 237 | ! Local: |
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| 238 | INTEGER :: n, i, j, k, l, m, sta(5), sto(5) |
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| 239 | REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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| 240 | REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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| 241 | REAL :: fm, ff, fp, dx |
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| 242 | !------------------------------------------------------------------------------- |
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| 243 | n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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| 244 | FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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| 245 | FORALL(i=2:n-1) |
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| 246 | h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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| 247 | END FORALL |
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| 248 | slopes5(:,:,:,:,:)=0. |
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| 249 | sta=[1,1,1,1,1]; sta(ix)=2 |
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| 250 | sto=SHAPE(f); sto(ix)=n-1 |
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| 251 | DO m=sta(5),sto(5); IF(ix==5) dx=delta_xc(m) |
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| 252 | DO l=sta(4),sto(4); IF(ix==4) dx=delta_xc(l) |
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| 253 | DO k=sta(3),sto(3); IF(ix==3) dx=delta_xc(k) |
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| 254 | DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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| 255 | DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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| 256 | ff=f(i,j,k,l,m) |
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| 257 | SELECT CASE(ix) |
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| 258 | CASE(1); fm=f(i-1,j,k,l,m); fp=f(i+1,j,k,l,m) |
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| 259 | CASE(2); fm=f(i,j-1,k,l,m); fp=f(i,j+1,k,l,m) |
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| 260 | CASE(3); fm=f(i,j,k-1,l,m); fp=f(i,j,k+1,l,m) |
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| 261 | CASE(4); fm=f(i,j,k,l-1,m); fp=f(i,j,k,l+1,m) |
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| 262 | CASE(5); fm=f(i,j,k,l,m-1); fp=f(i,j,k,l,m+1) |
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| 263 | END SELECT |
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| 264 | IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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| 265 | slopes5(i,j,k,l,m)=0.; CYCLE !--- Local extremum |
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| 266 | !--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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| 267 | slopes5(i,j,k,l,m)=(fp-fm)/dx |
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| 268 | !--- Slope limitation |
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| 269 | slopes5(i,j,k,l,m) = SIGN(MIN(ABS(slopes5(i,j,k,l,m)), & |
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| 270 | ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes5(i,j,k,l,m) ) |
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| 271 | END IF |
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| 272 | END DO |
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| 273 | END DO |
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| 274 | END DO |
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| 275 | END DO |
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| 276 | END DO |
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| 277 | DEALLOCATE(xc,h,delta_xc) |
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| 278 | |
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| 279 | END FUNCTION slopes5 |
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| 280 | ! |
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| 281 | !------------------------------------------------------------------------------- |
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| 282 | |
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| 283 | END MODULE slopes_m |
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