Merge branch 'master' into reconnection
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b4bc20036c
@ -367,6 +367,12 @@ module interpolations
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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 ("ocmp5", "OCMP5")
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name_rec = "5th order Optimized Compact Monotonicity Preserving"
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interfaces => interfaces_dir
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reconstruct_states => reconstruct_ocmp5
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order = 5
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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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@ -5318,6 +5324,160 @@ module interpolations
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!
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!===============================================================================
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!
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! subroutine RECONSTRUCT_OCMP5:
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! -----------------------------
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!
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! Subroutine reconstructs the interface states using the 5th order Optimized
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! Compact Reconstruction Monotonicity Preserving (CRMP) 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] Myeong-Hwan Ahn, Duck-Joo Lee,
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! "Modified Monotonicity Preserving Constraints for High-Resolution
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! Optimized Compact Scheme",
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! Journal of Scientific Computing,
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! 2020, vol. 83, p. 34
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! https://doi.org/10.1007/s10915-020-01221-0
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!
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!===============================================================================
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!
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subroutine reconstruct_ocmp5(h, fc, fl, fr)
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use algebra, only : tridiag
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implicit none
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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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integer :: n, i, iret
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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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real(kind=8), dimension(3), parameter :: &
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di = [ 5.0163016d-01, 1.0d+00, 2.5394716d-01 ]
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real(kind=8), dimension(5), parameter :: &
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ci5 = [-4.44553d-03,8.101861d-02, 9.9428149d-01, &
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6.6721233d-01, 1.751043d-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, 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 :: &
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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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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 right-hand side of the linear system
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!
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do i = ng, n - ng + 1
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r(i) = sum(ci5(:) * fc(i-2:i+2))
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end do
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! use explicit methods for ghost zones
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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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do i = 3, ng
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r(i) = sum(ce5(:) * fc(i-2:i+2))
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end do
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do i = n - ng, n - 2
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r(i) = sum(ce5(:) * fc(i-2:i+2))
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end do
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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 limiter
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!
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call mp_limiting(fc(:), u(:))
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! return the interpolated values of the left state
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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 integrals
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!
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fi(1:n) = fc(n:1:-1)
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! prepare the right-hand side of the linear system
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!
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do i = ng, n - ng + 1
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r(i) = sum(ci5(:) * fi(i-2:i+2))
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end do ! i = ng, n - ng + 1
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! use explicit methods for ghost zones
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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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do i = 3, ng
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r(i) = sum(ce5(:) * fi(i-2:i+2))
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end do
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do i = n - ng, n - 2
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r(i) = sum(ce5(:) * fi(i-2:i+2))
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end do
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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 limiter
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!
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call mp_limiting(fi(:), u(:))
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! return the interpolated values of the right state
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!
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fr(1:n-1) = u(n-1:1:-1)
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! update the extremum 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_ocmp5
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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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@ -6104,6 +6264,12 @@ module interpolations
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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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! [3] Myeong-Hwan Ahn, Duck-Joo Lee,
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! "Modified Monotonicity Preserving Constraints for High-Resolution
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! Optimized Compact Scheme",
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! Journal of Scientific Computing,
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! 2020, vol. 83, p. 34
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! https://doi.org/10.1007/s10915-020-01221-0
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!
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!===============================================================================
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!
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@ -6120,8 +6286,9 @@ module interpolations
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! local variables
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!
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integer :: n, i, im1, ip1, ip2
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real(kind=8) :: dq, ds, dc0, dc4, dm1, dp1, dml, dmr
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logical :: test
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integer :: n, i, im2, im1, ip1, ip2
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real(kind=8) :: dq, ds, dc0, dc4, dm1, dp1, dml, dmr, bt
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real(kind=8) :: qlc, qmd, qmp, qmn, qmx, qul
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! local vectors
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@ -6129,12 +6296,10 @@ module interpolations
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real(kind=8), dimension(0:size(qc)+2) :: dm
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!
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!-------------------------------------------------------------------------------
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!
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! get the input vector size
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!
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n = size(qc)
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! calculate derivatives
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! 1st order derivatives
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!
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dm(0 ) = 0.0d+00
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dm(1 ) = 0.0d+00
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@ -6142,7 +6307,7 @@ module interpolations
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dm(n+1) = 0.0d+00
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dm(n+2) = 0.0d+00
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! check monotonicity condition for all elements and apply limiting if required
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! check the monotonicity condition and apply limiting if necessary
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!
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do i = 1, n - 1
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@ -6159,6 +6324,7 @@ module interpolations
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if (ds > eps) then
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im2 = i - 2
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im1 = i - 1
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ip2 = i + 2
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@ -6174,6 +6340,17 @@ module interpolations
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qul = qc(i) + dq
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qlc = qc(i) + 0.5d+00 * dq + dml
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test = qc(i) > max(qc(im1), qc(ip1)) .and. &
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min(qc(im1), qc(ip1)) > max(qc(im2), qc(ip2))
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test = test .or. qc(i) < min(qc(im1), qc(ip1)) .and. &
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max(qc(im1), qc(ip1)) < min(qc(im2), qc(ip2))
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if (test) then
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if (qc(im2) <= qc(ip1) .and. qc(ip2) <= qc(im1)) then
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bt = dc0 / (qc(ip2) + qc(im2) - 2.0d+00 * qc(i))
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if (bt >= 3.0d-01) qlc = qc(im2)
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end if
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end if
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qmx = max(min(qc(i), qc(ip1), qmd), min(qc(i), qul, qlc))
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qmn = min(max(qc(i), qc(ip1), qmd), max(qc(i), qul, qlc))
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