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|
! Copyright (C) 2006 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 divergence_matrix_cg
use quadrature
use fields
use field_derivatives
use state_module
use futils
use fetools
use spud
use boundary_conditions
use global_parameters, only: OPTION_PATH_LEN
use transform_elements
use fldebug
use field_options, only: complete_field_path
use upwind_stabilisation
use equation_of_state
use multiphase_module
implicit none
private
public :: assemble_divergence_matrix_cg, assemble_compressible_divergence_matrix_cg
! Stabilisation schemes
integer, parameter :: STABILISATION_NONE = 0, &
& STABILISATION_STREAMLINE_UPWIND = 1, STABILISATION_SUPG = 2
! Stabilisation scheme
integer :: stabilisation_scheme
integer :: nu_bar_scheme
real :: nu_bar_scale
contains
subroutine assemble_divergence_matrix_cg(CT_m, state, ct_rhs, &
test_mesh, field, option_path, &
div_mass, grad_mass, &
div_mass_lumped,&
grad_mass_lumped, get_ct)
! inputs/outputs
! bucket full of fields
type(state_type), intent(inout) :: state
! the velocity divergence gradient matrices
type(block_csr_matrix), intent(inout) :: CT_m
type(scalar_field), intent(inout), optional :: ct_rhs
type(mesh_type), intent(in) :: test_mesh
type(vector_field), intent(inout) :: field
character(len=*), intent(in), optional :: option_path
type(csr_matrix), intent(inout), optional :: div_mass, grad_mass
type(scalar_field), intent(inout), optional :: div_mass_lumped, grad_mass_lumped
logical, intent(in), optional :: get_ct
! local
integer, dimension(:), pointer :: test_nodes, field_nodes
integer, dimension(:), allocatable :: test_nodes_bdy, field_nodes_bdy
real, dimension(:,:,:), allocatable :: ele_mat, ele_mat_bdy
type(element_type), pointer :: field_shape, test_shape
real, dimension(:,:,:), allocatable :: dfield_t
real, dimension(:,:,:), allocatable :: dtest_t
real, dimension(:), allocatable :: detwei, detwei_bdy
real, dimension(:,:), allocatable :: normal_bdy
! loop integers
integer :: ele, sele, dim
! pointer to coordinates
type(vector_field), pointer :: coordinate
character(len=OPTION_PATH_LEN) :: l_option_path
! integrate by parts
logical :: integrate_by_parts
integer, dimension(:,:), allocatable :: field_bc_type
type(vector_field) :: field_bc
real, dimension(:,:), allocatable :: div_mass_mat, grad_mass_mat
integer :: stat
logical :: l_get_ct
!! Multiphase variables
logical :: multiphase
! Volume fraction fields
type(scalar_field), pointer :: vfrac
type(scalar_field) :: nvfrac
type(element_type), pointer :: nvfrac_shape
! Transformed gradient function for the non-linear PhaseVolumeFraction.
real, dimension(:, :, :), allocatable :: dnvfrac_t
! =============================================================
! Subroutine to construct the matrix CT_m (a.k.a. C1/2/3T).
! =============================================================
ewrite(2,*) 'In assemble_divergence_matrix_cg'
if(present(get_ct)) then
l_get_ct = get_ct
else
l_get_ct = .true.
end if
if(present(option_path)) then
l_option_path = trim(option_path)
else
l_option_path = trim(field%option_path)
end if
coordinate=>extract_vector_field(state, "Coordinate")
integrate_by_parts=have_option(trim(complete_field_path(l_option_path, stat=stat))//&
&"/spatial_discretisation/continuous_galerkin/integrate_continuity_by_parts")&
.or. have_option(trim(complete_field_path(l_option_path, stat=stat))//&
&"/integrate_divergence_by_parts")&
.or. have_option(trim(complete_field_path(l_option_path, stat=stat))//&
&"/spatial_discretisation/continuous_galerkin/integrate_divergence_by_parts")&
.or. have_option(trim(complete_field_path(l_option_path, stat=stat))//&
&"/spatial_discretisation/discontinuous_galerkin")
ewrite(2,*) "Divergence is integrated by parts: ", integrate_by_parts
if(present(ct_rhs)) call zero(ct_rhs)
! Check if we need to multiply through by the non-linear volume fraction
if(option_count("/material_phase/vector_field::Velocity/prognostic") > 1) then
multiphase = .true.
vfrac => extract_scalar_field(state, "PhaseVolumeFraction")
call allocate(nvfrac, vfrac%mesh, "NonlinearPhaseVolumeFraction")
call zero(nvfrac)
call get_nonlinear_volume_fraction(state, nvfrac)
ewrite_minmax(nvfrac)
else
multiphase = .false.
nullify(vfrac)
end if
if (l_get_ct) then
! Clear memory of arrays being designed
call zero(CT_m)
if(present(div_mass)) call zero(div_mass)
if(present(grad_mass)) call zero(grad_mass)
if(present(div_mass_lumped)) call zero(div_mass_lumped)
if(present(grad_mass_lumped)) call zero(grad_mass_lumped)
allocate(dfield_t(ele_loc(field, 1), ele_ngi(field, 1), field%dim), &
dtest_t(ele_loc(test_mesh, 1), ele_ngi(test_mesh, 1), field%dim), &
ele_mat(field%dim, ele_loc(test_mesh, 1), ele_loc(field, 1)), &
detwei(ele_ngi(field, 1)), &
grad_mass_mat(ele_loc(field, 1), ele_loc(field, 1)), &
div_mass_mat(ele_loc(test_mesh, 1), ele_loc(test_mesh, 1)))
if(multiphase) then
allocate(dnvfrac_t(ele_loc(nvfrac,1), ele_ngi(nvfrac,1), field%dim))
end if
do ele=1, element_count(test_mesh)
test_nodes=>ele_nodes(test_mesh, ele)
field_nodes=>ele_nodes(field, ele)
test_shape=>ele_shape(test_mesh, ele)
field_shape=>ele_shape(field, ele)
if(integrate_by_parts) then
! transform the pressure derivatives into physical space
! (and get detwei)
call transform_to_physical(coordinate, ele, test_shape, &
dshape=dtest_t, detwei=detwei)
if(multiphase) then
ele_mat = -dshape_shape(dtest_t, field_shape, detwei*ele_val_at_quad(nvfrac, ele))
else
ele_mat = -dshape_shape(dtest_t, field_shape, detwei)
end if
else
! transform the velociy derivatives into physical space
! (and get detwei)
call transform_to_physical(coordinate, ele, field_shape, &
dshape=dfield_t, detwei=detwei)
if(multiphase) then
! Split up the divergence term div(vfrac*u) = vfrac*div(u) + u*grad(vfrac)
! If the field and nvfrac meshes are different, then we need to
! compute the derivatives of the nvfrac shape functions.
if(.not.(nvfrac%mesh == field%mesh)) then
nvfrac_shape => ele_shape(nvfrac%mesh, ele)
call transform_to_physical(coordinate, ele, nvfrac_shape, dshape=dnvfrac_t)
else
dnvfrac_t = dfield_t
end if
ele_mat = shape_dshape(test_shape, dfield_t, detwei*ele_val_at_quad(nvfrac, ele)) + &
shape_shape_vector(test_shape, field_shape, detwei, ele_grad_at_quad(nvfrac, ele, dnvfrac_t))
else
ele_mat = shape_dshape(test_shape, dfield_t, detwei)
end if
end if
do dim = 1, field%dim
call addto(ct_m, 1, dim, test_nodes, field_nodes, ele_mat(dim,:,:))
end do
if(present(div_mass).or.present(div_mass_lumped)) then
div_mass_mat = shape_shape(test_shape, test_shape, detwei)
if(present(div_mass)) then
call addto(div_mass, test_nodes, test_nodes, div_mass_mat)
end if
if(present(div_mass_lumped)) then
call addto(div_mass_lumped, test_nodes, sum(div_mass_mat, 2))
end if
end if
if(present(grad_mass).or.present(grad_mass_lumped)) then
grad_mass_mat = shape_shape(field_shape, field_shape, detwei)
if(present(grad_mass)) then
call addto(grad_mass, field_nodes, field_nodes, grad_mass_mat)
end if
if(present(grad_mass_lumped)) then
call addto(grad_mass_lumped, field_nodes, sum(grad_mass_mat, 2))
end if
end if
end do
if(multiphase) then
deallocate(dnvfrac_t)
end if
end if
if(integrate_by_parts) then
allocate(detwei_bdy(face_ngi(field, 1)), &
normal_bdy(field%dim, face_ngi(field, 1)))
allocate(field_nodes_bdy(field%mesh%faces%shape%loc))
allocate(test_nodes_bdy(test_mesh%faces%shape%loc))
allocate(ele_mat_bdy(field%dim, face_loc(test_mesh, 1), face_loc(field, 1)))
assert(surface_element_count(test_mesh)==surface_element_count(field))
allocate(field_bc_type(field%dim, surface_element_count(field)))
call get_entire_boundary_condition(field, (/ &
"weakdirichlet ", &
"no_normal_flow", &
"internal ", &
"free_surface "/), field_bc, field_bc_type)
do sele = 1, surface_element_count(test_mesh)
if(any(field_bc_type(:,sele)==2)&
.or.any(field_bc_type(:,sele)==3)&
.or.any(field_bc_type(:,sele)==4)) cycle
test_shape=>face_shape(test_mesh, sele)
field_shape=>face_shape(field, sele)
test_nodes_bdy=face_global_nodes(test_mesh, sele)
field_nodes_bdy=face_global_nodes(field, sele)
call transform_facet_to_physical(coordinate, sele, &
& detwei_f=detwei_bdy,&
& normal=normal_bdy)
if(multiphase) then
ele_mat_bdy = shape_shape_vector(test_shape, field_shape, detwei_bdy*face_val_at_quad(nvfrac, ele), normal_bdy)
else
ele_mat_bdy = shape_shape_vector(test_shape, field_shape, detwei_bdy, normal_bdy)
end if
do dim = 1, field%dim
if((field_bc_type(dim, sele)==1).and.present(ct_rhs)) then
call addto(ct_rhs, test_nodes_bdy, &
-matmul(ele_mat_bdy(dim,:,:), &
ele_val(field_bc, dim, sele)))
else
if (l_get_ct) then
call addto(ct_m, 1, dim, test_nodes_bdy, field_nodes_bdy, &
ele_mat_bdy(dim,:,:))
end if
end if
end do
end do
call deallocate(field_bc)
deallocate(field_bc_type)
deallocate(detwei_bdy, normal_bdy)
deallocate(test_nodes_bdy, field_nodes_bdy)
end if
if(multiphase) then
call deallocate(nvfrac)
end if
ewrite(2,*) 'Exiting assemble_divergence_matrix_cg'
end subroutine assemble_divergence_matrix_cg
subroutine assemble_compressible_divergence_matrix_cg(ctp_m, state, ct_rhs)
! inputs/outputs
! bucket full of fields
type(state_type), dimension(:), intent(inout) :: state
! the compressible divergence matrix
type(block_csr_matrix), intent(inout) :: ctp_m
type(scalar_field), intent(inout), optional :: ct_rhs
if((size(state)==1).and.(.not.has_scalar_field(state(1), "MaterialVolumeFraction"))) then
call assemble_1mat_compressible_divergence_matrix_cg(ctp_m, state(1), ct_rhs)
else
FLExit("Multimaterial compressible continuous_galerkin pressure not possible.")
end if
end subroutine assemble_compressible_divergence_matrix_cg
subroutine assemble_1mat_compressible_divergence_matrix_cg(ctp_m, state, ct_rhs)
! inputs/outputs
! bucket full of fields
type(state_type), intent(inout) :: state
! the compressible divergence matrix
type(block_csr_matrix), intent(inout) :: ctp_m
type(scalar_field), intent(inout), optional :: ct_rhs
! local
type(mesh_type), pointer :: test_mesh
type(vector_field), pointer :: field
integer, dimension(:), pointer :: test_nodes, field_nodes
integer, dimension(:), allocatable :: test_nodes_bdy, field_nodes_bdy
real, dimension(:,:,:), allocatable :: ele_mat, ele_mat_bdy
type(element_type), pointer :: field_shape, test_shape_ptr, density_shape
type(element_type) :: test_shape
real, dimension(:,:,:), allocatable :: dfield_t, dtest_t, ddensity_t
real, dimension(:), allocatable :: detwei, detwei_bdy, density_bdy
real, dimension(:,:,:), allocatable :: j_mat
real, dimension(:,:), allocatable :: normal_bdy
real, dimension(:), allocatable :: density_at_quad, olddensity_at_quad
real, dimension(:,:), allocatable :: density_grad_at_quad, nlvelocity_at_quad
! loop integers
integer :: ele, sele, dim
! pointer to coordinates
type(vector_field), pointer :: coordinate, nonlinearvelocity, velocity
type(scalar_field), pointer :: pressure, density, olddensity
real :: theta, dt
! integrate by parts
logical :: integrate_by_parts
integer, dimension(:,:), allocatable :: field_bc_type
type(vector_field) :: field_bc
integer, dimension(:), allocatable :: density_bc_type
type(scalar_field) :: density_bc
integer :: stat
! =============================================================
! Subroutine to construct the matrix ctp_m (a.k.a. C1/2/3TP).
! =============================================================
ewrite(2,*) 'In assemble_1mat_compressible_divergence_matrix_cg'
coordinate=> extract_vector_field(state, "Coordinate")
density => extract_scalar_field(state, "Density")
olddensity => extract_scalar_field(state, "OldDensity")
pressure => extract_scalar_field(state, "Pressure")
velocity=>extract_vector_field(state, "Velocity")
nonlinearvelocity=>extract_vector_field(state, "NonlinearVelocity") ! maybe this should be updated after the velocity solve?
integrate_by_parts=have_option(trim(complete_field_path(density%option_path, stat=stat))//&
&"/spatial_discretisation/continuous_galerkin/advection_terms/integrate_advection_by_parts")&
.or. have_option(trim(complete_field_path(velocity%option_path, stat=stat))//&
&"/spatial_discretisation/discontinuous_galerkin")
ewrite(2,*) "Compressible divergence is integrated by parts: ", integrate_by_parts
if(have_option(trim(density%option_path) // "/prognostic/spatial_discretisation/&
&continuous_galerkin/stabilisation/streamline_upwind")) then
ewrite(2, *) "Streamline upwind stabilisation"
FLExit("SU stabilisation broken with continuity at the moment.")
stabilisation_scheme = STABILISATION_STREAMLINE_UPWIND
call get_upwind_options(trim(density%option_path) // &
"/prognostic/spatial_discretisation/continuous_galerkin/&
&stabilisation/streamline_upwind", &
& nu_bar_scheme, nu_bar_scale)
else if(have_option(trim(density%option_path) // &
"/prognostic/spatial_discretisation/continuous_galerkin/&
&stabilisation/streamline_upwind_petrov_galerkin")) then
ewrite(2, *) "SUPG stabilisation"
stabilisation_scheme = STABILISATION_SUPG
call get_upwind_options(trim(density%option_path) // &
"/prognostic/spatial_discretisation/continuous_galerkin/&
&stabilisation/streamline_upwind_petrov_galerkin", &
& nu_bar_scheme, nu_bar_scale)
else
ewrite(2, *) "No stabilisation"
stabilisation_scheme = STABILISATION_NONE
end if
call get_option(trim(complete_field_path(density%option_path, stat=stat))//&
&"/temporal_discretisation/theta", theta)
call get_option("/timestepping/timestep", dt)
test_mesh => pressure%mesh
field => velocity
if(present(ct_rhs)) call zero(ct_rhs)
! Clear memory of arrays being designed
call zero(ctp_m)
allocate(dfield_t(ele_loc(field, 1), ele_ngi(field, 1), field%dim), &
dtest_t(ele_loc(test_mesh, 1), ele_ngi(test_mesh, 1), field%dim), &
ddensity_t(ele_loc(density, 1), ele_ngi(density, 1), field%dim), &
ele_mat(field%dim, ele_loc(test_mesh, 1), ele_loc(field, 1)), &
detwei(ele_ngi(field, 1)), &
density_at_quad(ele_ngi(density, 1)), &
olddensity_at_quad(ele_ngi(density, 1)), &
nlvelocity_at_quad(nonlinearvelocity%dim, ele_ngi(nonlinearvelocity, 1)), &
density_grad_at_quad(field%dim, ele_ngi(density,1)), &
j_mat(field%dim, field%dim, ele_ngi(density, 1)))
do ele=1, element_count(test_mesh)
test_nodes=>ele_nodes(test_mesh, ele)
field_nodes=>ele_nodes(field, ele)
test_shape_ptr => ele_shape(test_mesh, ele)
field_shape=>ele_shape(field, ele)
density_shape => ele_shape(density, ele)
density_at_quad = ele_val_at_quad(density, ele)
olddensity_at_quad = ele_val_at_quad(olddensity, ele)
nlvelocity_at_quad = ele_val_at_quad(nonlinearvelocity, ele)
if(any(stabilisation_scheme == (/STABILISATION_STREAMLINE_UPWIND, STABILISATION_SUPG/))) then
call transform_to_physical(coordinate, ele, test_shape_ptr, dshape = dtest_t, &
detwei = detwei, j = j_mat)
else
call transform_to_physical(coordinate, ele, test_shape_ptr, dshape = dtest_t, detwei=detwei)
end if
if(.not.integrate_by_parts) then
! transform the field (velocity) derivatives into physical space
call transform_to_physical(coordinate, ele, field_shape, dshape=dfield_t)
if(test_shape_ptr==density_shape) then
ddensity_t = dtest_t
else
call transform_to_physical(coordinate, ele, density_shape, dshape = ddensity_t)
end if
else
dfield_t = 0.0
ddensity_t = 0.0
end if
select case(stabilisation_scheme)
case(STABILISATION_SUPG)
test_shape = make_supg_shape(test_shape_ptr, dtest_t, nlvelocity_at_quad, j_mat, &
& nu_bar_scheme = nu_bar_scheme, nu_bar_scale = nu_bar_scale)
case default
test_shape = test_shape_ptr
call incref(test_shape)
end select
! Important note: with SUPG the test function derivatives have not been
! modified - i.e. dtest_t is currently used everywhere. This is fine for P1,
! but is not consistent for P>1.
if(integrate_by_parts) then
! if SUPG is fixed for P>1 then this dtest_t should be updated
ele_mat = -dshape_shape(dtest_t, field_shape, &
detwei*(theta*density_at_quad + (1-theta)*olddensity_at_quad))
else
density_grad_at_quad = theta*(ele_grad_at_quad(density, ele, ddensity_t))+&
(1-theta)*(ele_grad_at_quad(olddensity, ele, ddensity_t))
ele_mat = shape_dshape(test_shape, dfield_t, &
detwei*(theta*density_at_quad + (1-theta)*olddensity_at_quad)) + &
shape_shape_vector(test_shape, field_shape, detwei, density_grad_at_quad)
end if
! Stabilisation does not return the right shape for this operator!
select case(stabilisation_scheme)
case(STABILISATION_STREAMLINE_UPWIND)
! ele_mat = ele_mat + &
! & element_upwind_stabilisation_div(field_shape, ddensity_t, nlvelocity_at_quad, j_mat, detwei, &
! & nu_bar_scheme = nu_bar_scheme, nu_bar_scale = nu_bar_scale)
end select
do dim = 1, field%dim
call addto(ctp_m, 1, dim, test_nodes, field_nodes, ele_mat(dim,:,:))
end do
call deallocate(test_shape)
end do
if(integrate_by_parts) then
allocate(detwei_bdy(face_ngi(field, 1)), &
density_bdy(face_ngi(density, 1)), &
normal_bdy(field%dim, face_ngi(field, 1)))
allocate(field_nodes_bdy(field%mesh%faces%shape%loc))
allocate(test_nodes_bdy(test_mesh%faces%shape%loc))
allocate(ele_mat_bdy(field%dim, face_loc(test_mesh, 1), face_loc(field, 1)))
assert(surface_element_count(test_mesh)==surface_element_count(field))
allocate(field_bc_type(field%dim, surface_element_count(field)))
call get_entire_boundary_condition(field, (/ &
"weakdirichlet ", &
"no_normal_flow", &
"internal ", &
"free_surface "/), field_bc, field_bc_type)
allocate(density_bc_type(surface_element_count(density)))
call get_entire_boundary_condition(density, (/ &
"weakdirichlet"/), density_bc, density_bc_type)
do sele = 1, surface_element_count(test_mesh)
if(any(field_bc_type(:,sele)==2)&
.or.any(field_bc_type(:,sele)==3)&
.or.any(field_bc_type(:,sele)==4)) cycle
test_shape_ptr=>face_shape(test_mesh, sele)
field_shape=>face_shape(field, sele)
test_nodes_bdy=face_global_nodes(test_mesh, sele)
field_nodes_bdy=face_global_nodes(field, sele)
if(density_bc_type(sele)==1) then
! not considering time varying bc yet!
density_bdy = ele_val_at_quad(density_bc, sele)
else
density_bdy = theta*face_val_at_quad(density, sele) + &
(1-theta)*face_val_at_quad(olddensity, sele)
end if
call transform_facet_to_physical(coordinate, sele, &
& detwei_f=detwei_bdy,&
& normal=normal_bdy)
ele_mat_bdy = shape_shape_vector(test_shape_ptr, field_shape, &
detwei_bdy*density_bdy, normal_bdy)
do dim = 1, field%dim
if((field_bc_type(dim, sele)==1).and.present(ct_rhs)) then
call addto(ct_rhs, test_nodes_bdy, &
-matmul(ele_mat_bdy(dim,:,:), &
ele_val(field_bc, dim, sele)))
else
call addto(ctp_m, 1, dim, test_nodes_bdy, field_nodes_bdy, &
ele_mat_bdy(dim,:,:))
end if
end do
end do
call deallocate(field_bc)
call deallocate(density_bc)
deallocate(field_bc_type, density_bc_type)
deallocate(detwei_bdy, normal_bdy, density_bdy)
deallocate(test_nodes_bdy, field_nodes_bdy)
end if
end subroutine assemble_1mat_compressible_divergence_matrix_cg
end module divergence_matrix_cg
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