Merge branch 'master' into reconnection
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907e2afdab
@ -361,6 +361,12 @@ module interpolations
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reconstruct_states => reconstruct_crmp7
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order = 7
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nghosts = max(nghosts, 4)
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case ("crmp7l", "crmp7ld", "CRMP7L", "CRMP7LD")
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name_rec = "7th order Low-Dissipation Compact Monotonicity Preserving"
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interfaces => interfaces_dir
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reconstruct_states => reconstruct_crmp7ld
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order = 7
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nghosts = max(nghosts, 4)
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case ("gp", "GP")
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write(stmp, '(f16.1)') sgp
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write(name_rec, '("Gaussian Process (",i1,"-point, δ=",a,")")') ngp &
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@ -5129,6 +5135,189 @@ module interpolations
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!
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!===============================================================================
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!
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! subroutine RECONSTRUCT_CRMP7LD:
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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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! low dissipation Compact Reconstruction Monotonicity Preserving (CRMP)
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! 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_crmp7ld(h, fc, fl, fr)
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! include external procedures
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!
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use algebra , only : tridiag
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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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real(kind=8) , intent(in) :: h
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real(kind=8), dimension(:), intent(in) :: fc
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real(kind=8), dimension(:), intent(out) :: fl, fr
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! local variables
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!
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integer :: n, i, iret
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! local arrays for derivatives
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!
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real(kind=8), dimension(size(fc)) :: fi
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real(kind=8), dimension(size(fc)) :: a, b, c
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real(kind=8), dimension(size(fc)) :: r
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real(kind=8), dimension(size(fc)) :: u
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! local parameters
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!
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real(kind=8), dimension(3), parameter :: &
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di = [ 5.0d+00, 1.2d+01, 4.0d+00 ] / 2.1d+01
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real(kind=8), dimension(6), parameter :: &
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ci = [-2.00d+00, 4.20d+01, 6.37d+02, &
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5.57d+02, 2.70d+01,-1.00d+00 ] / 1.26d+03
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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, 4.70d+01, &
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2.70d+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 :: &
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ce2 = [ 5.0d-01, 5.0d-01 ]
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!
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!-------------------------------------------------------------------------------
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!
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! get the input vector length
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!
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n = size(fc)
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! prepare the diagonals of the tridiagonal matrix
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!
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do i = 1, ng
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a(i) = 0.0d+00
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b(i) = 1.0d+00
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c(i) = 0.0d+00
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end do
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do i = ng + 1, n - ng - 1
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a(i) = di(1)
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b(i) = di(2)
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c(i) = di(3)
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end do
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do i = n - ng, n
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a(i) = 0.0d+00
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b(i) = 1.0d+00
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c(i) = 0.0d+00
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end do
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!! === left-side interpolation ===
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!!
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! prepare the tridiagonal system coefficients for the interior part
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!
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do i = ng, n - ng + 1
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r(i) = sum( ci(:) * fc(i-2:i+3))
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end do
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! interpolate ghost zones using the explicit method
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!
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r( 1) = sum(ce2(:) * fc( 1: 2))
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r( 2) = sum(ce3(:) * fc( 1: 3))
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r( 3) = sum(ce5(:) * fc( 1: 5))
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do i = 4, ng
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r(i) = sum(ce7(:) * fc(i-3:i+3))
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end do
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do i = n - ng, n - 3
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r(i) = sum(ce7(:) * fc(i-3:i+3))
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end do
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r(n-2) = sum(ce5(:) * fc(n-4: n))
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r(n-1) = sum(ce3(:) * fc(n-2: n))
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r(n ) = fc(n )
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! solve the tridiagonal system of equations
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!
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call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n), iret)
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! apply the monotonicity preserving limiting
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!
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call mp_limiting(fc(:), u(:))
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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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! prepare the tridiagonal system coefficients for the interior part
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!
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do i = ng, n - ng + 1
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r(i) = sum( ci(:) * fi(i-2:i+3))
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end do ! i = ng, n - ng + 1
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! interpolate ghost zones using the explicit method
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!
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r( 1) = sum(ce2(:) * fi( 1: 2))
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r( 2) = sum(ce3(:) * fi( 1: 3))
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r( 3) = sum(ce5(:) * fi( 1: 5))
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do i = 4, ng
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r(i) = sum(ce7(:) * fi(i-3:i+3))
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end do
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do i = n - ng, n - 3
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r(i) = sum(ce7(:) * fi(i-3:i+3))
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end do
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r(n-2) = sum(ce5(:) * fi(n-4: n))
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r(n-1) = sum(ce3(:) * fi(n-2: n))
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r(n ) = fi(n )
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! solve the tridiagonal system of equations
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!
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call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n), iret)
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! apply the monotonicity preserving limiting
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!
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call mp_limiting(fi(:), u(:))
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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_crmp7ld
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!
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!===============================================================================
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!
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! subroutine PREPARE_GP:
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! ---------------------
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!
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