Merge branch 'master' into reconnection
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commit
ff3e0349ca
@ -264,6 +264,13 @@ module interpolations
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if (verbose .and. ng < 4) &
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call print_warning("interpolations:initialize_interpolation" &
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, "Increase the number of ghost cells (at least 4).")
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case ("mp7", "MP7")
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name_rec = "7th order Monotonicity Preserving"
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interfaces => interfaces_dir
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reconstruct_states => reconstruct_mp7
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if (verbose .and. ng < 4) &
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call print_warning("interpolations:initialize_interpolation" &
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, "Increase the number of ghost cells (at least 4).")
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case ("crmp5", "CRMP5")
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name_rec = "5th order Compact Monotonicity Preserving"
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interfaces => interfaces_dir
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@ -3397,7 +3404,7 @@ module interpolations
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!
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!===============================================================================
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!
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subroutine reconstruct_mp5(n, h, f, fl, fr)
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subroutine reconstruct_mp5(n, h, fc, fl, fr)
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! local variables are not implicit by default
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!
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@ -3407,134 +3414,88 @@ module interpolations
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!
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integer , intent(in) :: n
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real(kind=8) , intent(in) :: h
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real(kind=8), dimension(n), intent(in) :: f
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real(kind=8), dimension(n), intent(in) :: fc
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real(kind=8), dimension(n), intent(out) :: fl, fr
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! local variables
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!
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integer :: i, im1, ip1, im2, ip2
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real(kind=8) :: df, ds, dc0, dc4, dm1, dp1, dml, dmr
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real(kind=8) :: flc, fmd, fmp, fmn, fmx, ful
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real(kind=8) :: sigma
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integer :: i
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! local arrays for derivatives
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!
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real(kind=8), dimension(n) :: dfm, dfp
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real(kind=8), dimension(n) :: fi
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real(kind=8), dimension(n) :: u
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! local parameters
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!
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real(kind=8), dimension(5), parameter :: &
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ce5 = (/ 2.0d+00,-1.3d+01, 4.7d+01 &
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, 2.7d+01,-3.0d+00 /) / 6.0d+01
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real(kind=8), dimension(3), parameter :: &
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ce3 = (/-1.0d+00, 5.0d+00, 2.0d+00 /) / 6.0d+00
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real(kind=8), dimension(2), parameter :: ce2 = (/ 5.0d-01, 5.0d-01 /)
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!
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!-------------------------------------------------------------------------------
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!
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! calculate the left and right derivatives
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!! === left-side interpolation ===
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!!
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! reconstruct the interface state using the 5th order interpolation
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!
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do i = 1, n - 1
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ip1 = i + 1
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dfp(i ) = f(ip1) - f(i)
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dfm(ip1) = dfp(i)
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do i = 3, n - 2
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u(i) = sum(ce5(:) * fc(i-2:i+2))
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end do
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dfm(1) = dfp(1)
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dfp(n) = dfm(n)
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! obtain the face values using high order interpolation
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! interpolate the interface state of the ghost zones using the interpolations
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! of lower orders
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!
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do i = 2, n - 1
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u( 1) = sum(ce2(:) * fc( 1: 2))
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u( 2) = sum(ce3(:) * fc( 1: 3))
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u(n-1) = sum(ce3(:) * fc(n-2: n))
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u(n ) = fc(n )
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im2 = max(1, i - 2)
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im1 = i - 1
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ip1 = i + 1
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ip2 = min(n, i + 2)
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fl(i) = (4.7d+01 * f(i ) + (2.7d+01 * f(ip1) - 1.3d+01 * f(im1)) &
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- (3.0d+00 * f(ip2) - 2.0d+00 * f(im2))) &
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/ 6.0d+01
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fr(i) = (4.7d+01 * f(i ) + (2.7d+01 * f(im1) - 1.3d+01 * f(ip1)) &
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- (3.0d+00 * f(im2) - 2.0d+00 * f(ip2))) &
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/ 6.0d+01
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end do ! i = 2, n - 1
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! apply monotonicity preserving limiting
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! apply the monotonicity preserving limiting
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!
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do i = 2, n - 1
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call mp_limiting(n, fc(1:n), u(1:n))
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im1 = i - 1
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ip1 = i + 1
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if (dfm(i) * dfp(i) >= 0.0d+00) then
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sigma = kappa
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else
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sigma = kbeta
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end if
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! get the limiting condition for the left state
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! copy the interpolation to the respective vector
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!
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df = sigma * dfm(i)
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fmp = f(i) + minmod(dfp(i), df)
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ds = (fl(i) - f(i)) * (fl(i) - fmp)
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fl(1:n) = u(1:n)
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! limit the left state
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!! === right-side interpolation ===
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!!
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! invert the cell-centered value vector
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!
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if (ds > eps) then
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fi(1:n) = fc(n:1:-1)
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dm1 = dfp(im1) - dfm(im1)
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dc0 = dfp(i ) - dfm(i )
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dp1 = dfp(ip1) - dfm(ip1)
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dc4 = 4.0d+00 * dc0
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dml = 0.5d+00 * minmod4(dc4 - dm1, 4.0d+00 * dm1 - dc0, dc0, dm1)
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dmr = 0.5d+00 * minmod4(dc4 - dp1, 4.0d+00 * dp1 - dc0, dc0, dp1)
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fmd = f(i) + 0.5d+00 * dfp(i) - dmr
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ful = f(i) + df
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flc = f(i) + 0.5d+00 * df + dml
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fmx = max(min(f(i), f(ip1), fmd), min(f(i), ful, flc))
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fmn = min(max(f(i), f(ip1), fmd), max(f(i), ful, flc))
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fl(i) = median(fl(i), fmn, fmx)
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end if
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! get the limiting condition for the right state
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! reconstruct the interface state using the 5th order interpolation
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!
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df = sigma * dfp(i)
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fmp = f(i) - minmod(dfm(i), df)
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ds = (fr(i) - f(i)) * (fr(i) - fmp)
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do i = 3, n - 2
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u(i) = sum(ce5(:) * fi(i-2:i+2))
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end do
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! limit the right state
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! interpolate the interface state of the ghost zones using the interpolations
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! of lower orders
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!
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if (ds > eps) then
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u( 1) = sum(ce2(:) * fi( 1: 2))
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u( 2) = sum(ce3(:) * fi( 1: 3))
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u(n-1) = sum(ce3(:) * fi(n-2: n))
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u(n ) = fi(n )
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dm1 = dfp(im1) - dfm(im1)
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dc0 = dfp(i ) - dfm(i )
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dp1 = dfp(ip1) - dfm(ip1)
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dc4 = 4.0d+00 * dc0
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dml = 0.5d+00 * minmod4(dc4 - dm1, 4.0d+00 * dm1 - dc0, dc0, dm1)
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dmr = 0.5d+00 * minmod4(dc4 - dp1, 4.0d+00 * dp1 - dc0, dc0, dp1)
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fmd = f(i) - 0.5d+00 * dfm(i) - dml
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ful = f(i) - df
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flc = f(i) - 0.5d+00 * df + dmr
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fmx = max(min(f(i), f(im1), fmd), min(f(i), ful, flc))
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fmn = min(max(f(i), f(im1), fmd), max(f(i), ful, flc))
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fr(i) = median(fr(i), fmn, fmx)
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end if
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! shift the right state
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! apply the monotonicity preserving limiting
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!
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fr(im1) = fr(i)
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call mp_limiting(n, fi(1:n), u(1:n))
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end do ! n = 2, n - 1
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! copy the interpolation to the respective vector
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!
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fr(1:n-1) = u(n-1:1:-1)
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! update the interpolation of the first and last points
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!
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i = n - 1
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fl(1) = 0.5d+00 * (f(1) + f(2))
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fr(i) = 0.5d+00 * (f(i) + f(n))
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fl(n) = f(n)
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fr(n) = f(n)
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fl(1) = 0.5d+00 * (fc(1) + fc(2))
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fr(i) = 0.5d+00 * (fc(i) + fc(n))
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fl(n) = fc(n)
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fr(n) = fc(n)
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!-------------------------------------------------------------------------------
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!
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@ -3542,6 +3503,137 @@ module interpolations
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!
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!===============================================================================
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!
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! subroutine RECONSTRUCT_MP7:
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! --------------------------
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!
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! Subroutine reconstructs the interface states using the seventh order
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! Monotonicity Preserving (MP) method.
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!
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! Arguments are described in subroutine reconstruct().
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!
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! References:
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!
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! [1] Suresh, A. & Huynh, H. T.,
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! "Accurate Monotonicity-Preserving Schemes with Runge-Kutta
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! Time Stepping"
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! Journal on Computational Physics,
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! 1997, vol. 136, pp. 83-99,
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! http://dx.doi.org/10.1006/jcph.1997.5745
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! [2] He, ZhiWei, Li, XinLiang, Fu, DeXun, & Ma, YanWen,
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! "A 5th order monotonicity-preserving upwind compact difference
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! scheme",
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! Science China Physics, Mechanics and Astronomy,
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! Volume 54, Issue 3, pp. 511-522,
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! http://dx.doi.org/10.1007/s11433-010-4220-x
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!
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!===============================================================================
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!
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subroutine reconstruct_mp7(n, h, fc, fl, fr)
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! local variables are not implicit by default
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!
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implicit none
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! subroutine arguments
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!
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integer , intent(in) :: n
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real(kind=8) , intent(in) :: h
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real(kind=8), dimension(n), intent(in) :: fc
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real(kind=8), dimension(n), intent(out) :: fl, fr
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! local variables
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!
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integer :: i
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! local arrays for derivatives
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!
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real(kind=8), dimension(n) :: fi
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real(kind=8), dimension(n) :: u
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! local parameters
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!
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real(kind=8), dimension(7), parameter :: &
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ce7 = (/-3.0d+00, 2.5d+01,-1.01d+02, 3.19d+02 &
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, 2.14d+02,-3.8d+01, 4.0d+00 /) / 4.2d+02
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real(kind=8), dimension(5), parameter :: &
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ce5 = (/ 2.0d+00,-1.3d+01, 4.7d+01 &
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, 2.7d+01,-3.0d+00 /) / 6.0d+01
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real(kind=8), dimension(3), parameter :: &
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ce3 = (/-1.0d+00, 5.0d+00, 2.0d+00 /) / 6.0d+00
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real(kind=8), dimension(2), parameter :: ce2 = (/ 5.0d-01, 5.0d-01 /)
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!
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!-------------------------------------------------------------------------------
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!
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!! === left-side interpolation ===
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!!
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! reconstruct the interface state using the 5th order interpolation
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!
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do i = 4, n - 3
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u(i) = sum(ce7(:) * fc(i-3:i+3))
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end do
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! interpolate the interface state of the ghost zones using the interpolations
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! of lower orders
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!
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u( 1) = sum(ce2(:) * fc( 1: 2))
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u( 2) = sum(ce3(:) * fc( 1: 3))
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u( 3) = sum(ce5(:) * fc( 1: 5))
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u(n-2) = sum(ce5(:) * fc(n-4: n))
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u(n-1) = sum(ce3(:) * fc(n-2: n))
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u(n ) = fc(n )
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! apply the monotonicity preserving limiting
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!
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call mp_limiting(n, fc(1:n), u(1:n))
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! copy the interpolation to the respective vector
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!
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fl(1:n) = u(1:n)
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!! === right-side interpolation ===
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!!
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! invert the cell-centered value vector
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!
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fi(1:n) = fc(n:1:-1)
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! reconstruct the interface state using the 5th order interpolation
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!
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do i = 4, n - 3
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u(i) = sum(ce7(:) * fi(i-3:i+3))
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end do
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! interpolate the interface state of the ghost zones using the interpolations
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! of lower orders
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!
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u( 1) = sum(ce2(:) * fi( 1: 2))
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u( 2) = sum(ce3(:) * fi( 1: 3))
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u( 3) = sum(ce5(:) * fi( 1: 5))
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u(n-2) = sum(ce5(:) * fi(n-4: n))
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u(n-1) = sum(ce3(:) * fi(n-2: n))
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u(n ) = fi(n )
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! apply the monotonicity preserving limiting
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!
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call mp_limiting(n, fi(1:n), u(1:n))
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! copy the interpolation to the respective vector
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!
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fr(1:n-1) = u(n-1:1:-1)
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! update the interpolation of the first and last points
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!
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i = n - 1
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fl(1) = 0.5d+00 * (fc(1) + fc(2))
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fr(i) = 0.5d+00 * (fc(i) + fc(n))
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fl(n) = fc(n)
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fr(n) = fc(n)
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!-------------------------------------------------------------------------------
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!
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end subroutine reconstruct_mp7
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!
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!===============================================================================
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!
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! subroutine RECONSTRUCT_CRMP5:
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! ----------------------------
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!
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@ -3583,6 +3675,7 @@ module interpolations
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real(kind=8) , intent(in) :: h
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real(kind=8), dimension(n), intent(in) :: fc
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real(kind=8), dimension(n), intent(out) :: fl, fr
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! local variables
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!
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integer :: i
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Reference in New Issue
Block a user