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! Copyright (C) 2010 Imperial College London and others.
!
! Please see the AUTHORS file in the main source directory for a full list
! of copyright holders.
!
! Prof. C Pain
! Applied Modelling and Computation Group
! Department of Earth Science and Engineering
! Imperial College London
!
! amcgsoftware@imperial.ac.uk
!
! This library is free software; you can redistribute it and/or
! modify it under the terms of the GNU Lesser General Public
! License as published by the Free Software Foundation,
! version 2.1 of the License.
!
! This library is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
! Lesser General Public License for more details.
!
! You should have received a copy of the GNU Lesser General Public
! License along with this library; if not, write to the Free Software
! Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
! USA
#include "fdebug.h"
module streamfunction
use state_module
use fields
use sparse_tools
use spud
use global_parameters, only: OPTION_PATH_LEN
use sparsity_patterns
use solvers
use boundary_conditions
use vector_tools
use transform_elements
use eventcounter
use sparsity_patterns_meshes
USE parallel_fields
USE Parallel_Tools
implicit none
private
public :: calculate_stream_function_multipath_2d
type(integer_vector), dimension(:), allocatable, save :: flux_face_list
real, dimension(:,:), allocatable, save :: flux_normal
integer, save :: last_adapt=-1
contains
subroutine find_stream_paths(X, streamfunc)
!!< Find the paths through the mesh over which the velocity will be
!!< integrated to calculate the flux.
type(vector_field), intent(in) :: X
type(scalar_field), intent(inout) :: streamfunc
type(ilist) :: tmp_face_list
integer :: bc_count
character(len=OPTION_PATH_LEN) :: option_path
real, dimension(2) :: start, end, dx, face_c
integer, dimension(:), pointer :: neigh
integer :: face, p, ele1, ele2, e2, i
real :: dx2, c1, c2
bc_count=get_boundary_condition_count(streamfunc)
if(.not.(allocated(flux_face_list))) then
allocate(flux_face_list(bc_count))
CALL nullify(flux_face_list)
allocate(flux_normal(2, bc_count))
end if
bc_loop: do i=1, bc_count
call get_boundary_condition(streamfunc, i, option_path=option_path)
if (have_option(trim(option_path)//"/primary_boundary")) then
! No path on the primary boundary.
if (associated(flux_face_list(i)%ptr)) then
deallocate(flux_face_list(i)%ptr)
end if
allocate(flux_face_list(i)%ptr(0))
cycle bc_loop
end if
! We must be on a secondary boundary.
call get_option(trim(option_path)//"/secondary_boundary/primary_point"&
&, start)
call get_option(trim(option_path)//"/secondary_boundary/secondary_point"&
&, end)
dx=-abs(start-end)
dx2=dot_product(dx,dx)
do ele1=1, element_count(streamfunc)
neigh=>ele_neigh(X, ele1)
do e2=1,size(neigh)
ele2=neigh(e2)
! Don't do boundaries
if (ele2<=0) cycle
! Do each edge only once
if (ele1>ele2) cycle
!for parallel check that we own the node
if (.not.element_owned(streamfunc, ele1)) cycle
face=ele_face(streamfunc, ele1, ele2)
face_c=sum(face_val(X,face),2)/face_loc(X,face)
p=dot_product(face_c,dx)/dx2
! If the face is not within the limits of the line, don't do it.
if (p<0.or.p>1) cycle
c1=cross_product2(sum(ele_val(X,ele1),2)/ele_loc(X,ele1)-start, dx)
c2=cross_product2(sum(ele_val(X,ele2),2)/ele_loc(X,ele2)-start, dx)
if(C1<0 .and. C2>=0) then
continue
else if (C1>=0 .and. C2<0) then
continue
else
cycle
end if
call insert(tmp_face_list, face)
end do
end do
if (associated(flux_face_list(i)%ptr)) then
deallocate(flux_face_list(i)%ptr)
end if
allocate(flux_face_list(i)%ptr(tmp_face_list%length))
flux_face_list(i)%ptr=list2vector(tmp_face_list)
call flush_list(tmp_face_list)
! Work out the orthonormal to the line.
dx=start-end
dx=dx/sqrt(dx2)
flux_normal(:,i)=(/-dx(2), dx(1)/)
end do bc_loop
end subroutine find_stream_paths
function boundary_value(X, U, bc_num)
!!< Calculate the value of the streamfunction on the boundary provided
!!< by integrating the velocity flux across a line between this
!!< boundary and the primary boundary.
real :: boundary_value
type(vector_field), intent(in) :: X, U
integer, intent(in) :: bc_num
integer :: face, i
boundary_value=0.0
do i=1, size(flux_face_list(bc_num)%ptr)
face=flux_face_list(bc_num)%ptr(i)
boundary_value=boundary_value + face_flux(face, X, U, bc_num)
end do
! for parallel so each partitition calculates the bit of the flux that it owns and they sum along the boundary so they all have the correct bd. condition
call allsum(boundary_value)
contains
function face_flux(face, X, U, bc_num)
real :: face_flux
integer, intent(in) :: face, bc_num
type(vector_field), intent(in) :: X, U
real, dimension(face_ngi(U, face)) :: detwei
real, dimension(U%dim,face_ngi(U, face)) :: normal, U_quad
integer :: gi
call transform_facet_to_physical(X, face, detwei_f=detwei, normal=normal)
U_quad=face_val_at_quad(U,face)
face_flux=0.0
do gi=1, size(detwei)
face_flux=face_flux+abs(dot_product(flux_normal(:,bc_num),normal(:,gi)))&
* dot_product(U_quad(:,gi),flux_normal(:,bc_num))&
* detwei(gi)
end do
end function face_flux
end function boundary_value
subroutine calculate_stream_function_multipath_2d(state, streamfunc)
!!< Calculate the stream function for a
type(state_type), intent(inout) :: state
type(scalar_field), intent(inout) :: streamfunc
integer :: i, ele, stat
type(vector_field), pointer :: X, U
type(csr_sparsity), pointer :: psi_sparsity
type(csr_matrix) :: psi_mat
type(scalar_field) :: rhs
real :: flux_val
type(scalar_field), pointer :: surface_field
integer :: mesh_movement
integer, save :: last_mesh_movement = -1
X => extract_vector_field(state, "Coordinate", stat)
if(present_and_nonzero(stat)) return
U => extract_vector_field(state, "Velocity", stat)
if(present_and_nonzero(stat)) return
if (X%dim/=2) then
FLExit("Streamfunction is only valid in 2d")
end if
! No discontinuous stream functions.
if (continuity(streamfunc)<0) then
FLExit("Streamfunction must be a continuous field")
end if
if (last_adapt<eventcount(EVENT_ADAPTIVITY)) then
last_adapt=eventcount(EVENT_ADAPTIVITY)
call find_stream_paths(X, streamfunc)
end if
psi_mat = extract_csr_matrix(state, "StreamFunctionMatrix", stat = stat)
if(stat == 0) then
mesh_movement = eventcount(EVENT_MESH_MOVEMENT)
if(mesh_movement /= last_mesh_movement) then
stat = 1
end if
end if
if(stat /= 0) then
psi_sparsity => get_csr_sparsity_firstorder(state, streamfunc%mesh, streamfunc%mesh)
call allocate(psi_mat, psi_sparsity, name="StreamFunctionMatrix")
call zero(psi_mat)
call allocate(rhs, streamfunc%mesh, "StreamFunctionRHS")
call zero(rhs)
do ele=1, element_count(streamfunc)
call calculate_streamfunc_ele(rhs, ele, X, U, psi_mat = psi_mat)
end do
call insert(state, psi_mat, psi_mat%name)
else
call incref(psi_mat)
call allocate(rhs, streamfunc%mesh, "StreamFunctionRHS")
call zero(rhs)
do ele=1, element_count(streamfunc)
call calculate_streamfunc_ele(rhs, ele, X, U)
end do
end if
last_mesh_movement = eventcount(EVENT_MESH_MOVEMENT)
do i = 1, get_boundary_condition_count(streamfunc)
surface_field=>extract_surface_field(streamfunc, i, "value")
flux_val=boundary_value(X,U,i)
call set(surface_field, flux_val)
end do
call zero(streamfunc)
call apply_dirichlet_conditions(psi_mat, rhs, streamfunc)
call petsc_solve(streamfunc, psi_mat, rhs)
call deallocate(rhs)
call deallocate(psi_mat)
contains
subroutine calculate_streamfunc_ele(rhs, ele, X, U, psi_mat)
type(scalar_field), intent(inout) :: rhs
type(vector_field), intent(in) :: X,U
integer, intent(in) :: ele
type(csr_matrix), optional, intent(inout) :: psi_mat
! Transformed gradient function for velocity.
real, dimension(ele_loc(U, ele), ele_ngi(U, ele), mesh_dim(U)) :: du_t
! Ditto for the stream function, psi
real, dimension(ele_loc(rhs, ele), ele_ngi(rhs, ele), mesh_dim(rhs))&
& :: dpsi_t
! Local vorticity_matrix
real, dimension(2, ele_loc(rhs, ele), ele_loc(U, ele)) ::&
& lvorticity_mat
! Local vorticity
real, dimension(ele_loc(rhs, ele)) :: lvorticity
! Variable transform times quadrature weights.
real, dimension(ele_ngi(U,ele)) :: detwei
type(element_type), pointer :: U_shape, psi_shape
integer, dimension(:), pointer :: psi_ele
integer :: i
U_shape=> ele_shape(U, ele)
psi_shape=> ele_shape(rhs, ele)
psi_ele=>ele_nodes(rhs, ele)
! Transform U derivatives and weights into physical space.
call transform_to_physical(X, ele, U_shape, dshape=du_t, detwei=detwei)
! Ditto psi.
call transform_to_physical(X, ele, psi_shape, dshape=dpsi_t)
if(present(psi_mat)) then
call addto(psi_mat, psi_ele, psi_ele, &
dshape_dot_dshape(dpsi_t, dpsi_t, detwei))
end if
lvorticity_mat=shape_curl_shape_2d(psi_shape, du_t, detwei)
lvorticity=0.0
do i=1,2
lvorticity=lvorticity &
+matmul(lvorticity_mat(i,:,:), ele_val(U, i, ele))
end do
call addto(rhs, psi_ele, -lvorticity)
end subroutine calculate_streamfunc_ele
end subroutine calculate_stream_function_multipath_2d
end module streamfunction
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