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MODULE slopes_m |
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! Author: Lionel GUEZ |
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! Extension / factorisation: David CUGNET |
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IMPLICIT NONE |
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! Those generic function computes second order slopes with Van |
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! Leer slope-limiting, given cell averages. Reference: Dukowicz, |
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! 1987, SIAM Journal on Scientific and Statistical Computing, 8, |
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! 305. |
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! The only difference between the specific functions is the rank |
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! of the first argument and the equal rank of the result. |
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! slope(ix,...) acts on ix th dimension. |
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! real, intent(in), rank >= 1:: f ! (n, ...) cell averages, n must be >= 1 |
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! real, intent(in):: x(:) ! (n + 1) cell edges |
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! real slopes, same shape as f ! (n, ...) |
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INTERFACE slopes |
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MODULE procedure slopes1, slopes2, slopes3, slopes4, slopes5 |
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END INTERFACE |
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PRIVATE |
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PUBLIC :: slopes |
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CONTAINS |
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!------------------------------------------------------------------------------- |
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! |
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PURE FUNCTION slopes1(ix, f, x) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: f(:) |
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REAL, INTENT(IN) :: x(:) |
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REAL :: slopes1(SIZE(f,1)) |
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!------------------------------------------------------------------------------- |
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! Local: |
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INTEGER :: n, i, j, sta(2), sto(2) |
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REAL :: xc(SIZE(f,1)) ! (n) cell centers |
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REAL :: h(2:SIZE(f,1)-1), delta_xc(2:SIZE(f,1)-1) ! (2:n-1) |
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REAL :: fm, ff, fp, dx |
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!------------------------------------------------------------------------------- |
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n=SIZE(f,ix) |
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FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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FORALL(i=2:n-1) |
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h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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END FORALL |
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slopes1(:)=0. |
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DO i=2,n-1 |
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ff=f(i); fm=f(i-1); fp=f(i+1) |
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IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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slopes1(i)=0.; CYCLE !--- Local extremum |
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!--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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slopes1(i)=(fp-fm)/delta_xc(i) |
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!--- Slope limitation |
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slopes1(i) = SIGN(MIN(ABS(slopes1(i)), & |
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ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes1(i) ) |
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END IF |
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END DO |
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END FUNCTION slopes1 |
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! |
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!------------------------------------------------------------------------------- |
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!------------------------------------------------------------------------------- |
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! |
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PURE FUNCTION slopes2(ix, f, x) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: f(:, :) |
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REAL, INTENT(IN) :: x(:) |
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REAL :: slopes2(SIZE(f,1),SIZE(f,2)) |
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!------------------------------------------------------------------------------- |
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! Local: |
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INTEGER :: n, i, j, sta(2), sto(2) |
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REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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REAL :: fm, ff, fp, dx |
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!------------------------------------------------------------------------------- |
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n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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FORALL(i=2:n-1) |
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h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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END FORALL |
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slopes2(:,:)=0. |
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sta=[1,1]; sta(ix)=2 |
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sto=SHAPE(f); sto(ix)=n-1 |
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DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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ff=f(i,j) |
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SELECT CASE(ix) |
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CASE(1); fm=f(i-1,j); fp=f(i+1,j) |
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CASE(2); fm=f(i,j-1); fp=f(i,j+1) |
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END SELECT |
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IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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slopes2(i,j)=0.; CYCLE !--- Local extremum |
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!--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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slopes2(i,j)=(fp-fm)/dx |
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!--- Slope limitation |
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slopes2(i,j) = SIGN(MIN(ABS(slopes2(i,j)), & |
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ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes2(i,j) ) |
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END IF |
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END DO |
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END DO |
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DEALLOCATE(xc,h,delta_xc) |
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END FUNCTION slopes2 |
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! |
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!------------------------------------------------------------------------------- |
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!------------------------------------------------------------------------------- |
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! |
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PURE FUNCTION slopes3(ix, f, x) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: f(:, :, :) |
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REAL, INTENT(IN) :: x(:) |
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REAL :: slopes3(SIZE(f,1),SIZE(f,2),SIZE(f,3)) |
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!------------------------------------------------------------------------------- |
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! Local: |
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INTEGER :: n, i, j, k, sta(3), sto(3) |
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REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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REAL :: fm, ff, fp, dx |
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!------------------------------------------------------------------------------- |
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n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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FORALL(i=2:n-1) |
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h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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END FORALL |
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slopes3(:,:,:)=0. |
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sta=[1,1,1]; sta(ix)=2 |
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sto=SHAPE(f); sto(ix)=n-1 |
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DO k=sta(3),sto(3); IF(ix==3) dx=delta_xc(k) |
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DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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ff=f(i,j,k) |
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SELECT CASE(ix) |
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CASE(1); fm=f(i-1,j,k); fp=f(i+1,j,k) |
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CASE(2); fm=f(i,j-1,k); fp=f(i,j+1,k) |
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CASE(3); fm=f(i,j,k-1); fp=f(i,j,k+1) |
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END SELECT |
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IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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slopes3(i,j,k)=0.; CYCLE !--- Local extremum |
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!--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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slopes3(i,j,k)=(fp-fm)/dx |
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!--- Slope limitation |
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slopes3(i,j,k) = SIGN(MIN(ABS(slopes3(i,j,k)), & |
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ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes3(i,j,k) ) |
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END IF |
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END DO |
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END DO |
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END DO |
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DEALLOCATE(xc,h,delta_xc) |
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END FUNCTION slopes3 |
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! |
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!------------------------------------------------------------------------------- |
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!------------------------------------------------------------------------------- |
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! |
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PURE FUNCTION slopes4(ix, f, x) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: f(:, :, :, :) |
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REAL, INTENT(IN) :: x(:) |
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REAL :: slopes4(SIZE(f,1),SIZE(f,2),SIZE(f,3),SIZE(f,4)) |
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!------------------------------------------------------------------------------- |
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! Local: |
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INTEGER :: n, i, j, k, l, m, sta(4), sto(4) |
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REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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REAL :: fm, ff, fp, dx |
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!------------------------------------------------------------------------------- |
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n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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FORALL(i=2:n-1) |
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h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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END FORALL |
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slopes4(:,:,:,:)=0. |
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sta=[1,1,1,1]; sta(ix)=2 |
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sto=SHAPE(f); sto(ix)=n-1 |
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DO l=sta(4),sto(4); IF(ix==4) dx=delta_xc(l) |
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DO k=sta(3),sto(3); IF(ix==3) dx=delta_xc(k) |
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DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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ff=f(i,j,k,l) |
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SELECT CASE(ix) |
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CASE(1); fm=f(i-1,j,k,l); fp=f(i+1,j,k,l) |
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CASE(2); fm=f(i,j-1,k,l); fp=f(i,j+1,k,l) |
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CASE(3); fm=f(i,j,k-1,l); fp=f(i,j,k+1,l) |
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CASE(4); fm=f(i,j,k,l-1); fp=f(i,j,k,l+1) |
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END SELECT |
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IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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slopes4(i,j,k,l)=0.; CYCLE !--- Local extremum |
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!--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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slopes4(i,j,k,l)=(fp-fm)/dx |
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!--- Slope limitation |
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slopes4(i,j,k,l) = SIGN(MIN(ABS(slopes4(i,j,k,l)), & |
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ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes4(i,j,k,l) ) |
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END IF |
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END DO |
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END DO |
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END DO |
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END DO |
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DEALLOCATE(xc,h,delta_xc) |
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END FUNCTION slopes4 |
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! |
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!------------------------------------------------------------------------------- |
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!------------------------------------------------------------------------------- |
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! |
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PURE FUNCTION slopes5(ix, f, x) |
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! |
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!------------------------------------------------------------------------------- |
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! Arguments: |
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INTEGER, INTENT(IN) :: ix |
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REAL, INTENT(IN) :: f(:, :, :, :, :) |
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REAL, INTENT(IN) :: x(:) |
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REAL :: slopes5(SIZE(f,1),SIZE(f,2),SIZE(f,3),SIZE(f,4),SIZE(f,5)) |
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!------------------------------------------------------------------------------- |
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! Local: |
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INTEGER :: n, i, j, k, l, m, sta(5), sto(5) |
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REAL, ALLOCATABLE :: xc(:) ! (n) cell centers |
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REAL, ALLOCATABLE :: h(:), delta_xc(:) ! (2:n-1) |
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REAL :: fm, ff, fp, dx |
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!------------------------------------------------------------------------------- |
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n=SIZE(f,ix); ALLOCATE(xc(n),h(2:n-1),delta_xc(2:n-1)) |
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FORALL(i=1:n) xc(i)=(x(i)+x(i+1))/2. |
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FORALL(i=2:n-1) |
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h(i)=ABS(x(i+1)-xc(i)) ; delta_xc(i)=xc(i+1)-xc(i-1) |
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END FORALL |
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slopes5(:,:,:,:,:)=0. |
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sta=[1,1,1,1,1]; sta(ix)=2 |
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sto=SHAPE(f); sto(ix)=n-1 |
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DO m=sta(5),sto(5); IF(ix==5) dx=delta_xc(m) |
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DO l=sta(4),sto(4); IF(ix==4) dx=delta_xc(l) |
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DO k=sta(3),sto(3); IF(ix==3) dx=delta_xc(k) |
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DO j=sta(2),sto(2); IF(ix==2) dx=delta_xc(j) |
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DO i=sta(1),sto(1); IF(ix==1) dx=delta_xc(i) |
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ff=f(i,j,k,l,m) |
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SELECT CASE(ix) |
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CASE(1); fm=f(i-1,j,k,l,m); fp=f(i+1,j,k,l,m) |
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CASE(2); fm=f(i,j-1,k,l,m); fp=f(i,j+1,k,l,m) |
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CASE(3); fm=f(i,j,k-1,l,m); fp=f(i,j,k+1,l,m) |
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CASE(4); fm=f(i,j,k,l-1,m); fp=f(i,j,k,l+1,m) |
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CASE(5); fm=f(i,j,k,l,m-1); fp=f(i,j,k,l,m+1) |
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END SELECT |
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IF(ff>=MAX(fm,fp).OR.ff<=MIN(fm,fp)) THEN |
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slopes5(i,j,k,l,m)=0.; CYCLE !--- Local extremum |
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!--- 2nd order slope ; (fm, ff, fp) strictly monotonous |
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slopes5(i,j,k,l,m)=(fp-fm)/dx |
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!--- Slope limitation |
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slopes5(i,j,k,l,m) = SIGN(MIN(ABS(slopes5(i,j,k,l,m)), & |
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ABS(fp-ff)/h(i),ABS(ff-fm)/h(i)),slopes5(i,j,k,l,m) ) |
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END IF |
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END DO |
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END DO |
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END DO |
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END DO |
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END DO |
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DEALLOCATE(xc,h,delta_xc) |
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END FUNCTION slopes5 |
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! |
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!------------------------------------------------------------------------------- |
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END MODULE slopes_m |
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