scalar_scheme.f90

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! todo: module name
module scalar_scheme
  use gather_scatter, only : gs_t
  use checkpoint, only : chkp_t
  use num_types, only: rp
  use field, only : field_t
  use field_list, only: field_list_t
  use space, only : space_t
  use dofmap, only : dofmap_t
  use krylov, only : ksp_t, krylov_solver_factory, krylov_solver_destroy, &
       ksp_max_iter
  use coefs, only : coef_t
  use dirichlet, only : dirichlet_t
  use neumann, only : neumann_t
  use jacobi, only : jacobi_t
  use device_jacobi, only : device_jacobi_t
  use sx_jacobi, only : sx_jacobi_t
  use hsmg, only : hsmg_t
  use precon, only : pc_t, precon_factory, precon_destroy
  use bc, only : bc_t, bc_list_t, bc_list_free, bc_list_init, &
       bc_list_apply_scalar, bc_list_add
  use field_dirichlet, only: field_dirichlet_t, field_dirichlet_update
  use mesh, only : mesh_t, neko_msh_max_zlbls, neko_msh_max_zlbl_len
  use facet_zone, only : facet_zone_t
  use time_scheme_controller, only : time_scheme_controller_t
  use logger, only : neko_log, log_size, neko_log_verbose
  use field_registry, only : neko_field_registry
  use usr_scalar, only : usr_scalar_t, usr_scalar_bc_eval
  use json_utils, only : json_get, json_get_or_default
  use json_module, only : json_file
  use user_intf, only : user_t, dummy_user_material_properties, &
                        user_material_properties
  use utils, only : neko_error
  use comm, only: neko_comm, mpi_integer, mpi_sum
  use scalar_source_term, only : scalar_source_term_t
  use math, only : cfill, add2s2
  use device_math, only : device_cfill, device_add2s2
  use neko_config, only : neko_bcknd_device
  use field_series, only : field_series_t
  use time_step_controller, only : time_step_controller_t
  use gradient_jump_penalty, only : gradient_jump_penalty_t
  implicit none
 
  type, abstract :: scalar_scheme_t
     type(field_t), pointer :: u
     type(field_t), pointer :: v
     type(field_t), pointer :: w
     type(field_t), pointer :: s
     type(field_series_t) :: slag
     type(space_t), pointer :: xh
     type(dofmap_t), pointer :: dm_xh
     type(gs_t), pointer :: gs_xh
     type(coef_t), pointer :: c_xh
     type(field_t), pointer :: f_xh => null()
     type(scalar_source_term_t) :: source_term
     class(ksp_t), allocatable :: ksp
     integer :: ksp_maxiter
     integer :: projection_dim
     
     integer :: projection_activ_step
     class(pc_t), allocatable :: pc
     type(dirichlet_t) :: dir_bcs(neko_msh_max_zlbls)
     type(field_dirichlet_t) :: field_dir_bc
     type(bc_list_t) :: field_dirichlet_bcs
     type(neumann_t) :: neumann_bcs(neko_msh_max_zlbls)
     type(usr_scalar_t) :: user_bc
     integer :: n_dir_bcs = 0
     integer :: n_neumann_bcs = 0
     type(bc_list_t) :: bclst_dirichlet
     type(bc_list_t) :: bclst_neumann
     type(json_file), pointer :: params
     type(mesh_t), pointer :: msh => null()
     type(chkp_t) :: chkp
     real(kind=rp) :: lambda
     type(field_t) :: lambda_field
     character(len=:), allocatable :: nut_field_name
     real(kind=rp) :: rho
     real(kind=rp) :: cp
     real(kind=rp) :: pr_turb
     logical :: variable_material_properties = .false.
     character(len=NEKO_MSH_MAX_ZLBL_LEN), allocatable :: bc_labels(:)
     logical :: if_gradient_jump_penalty
     type(gradient_jump_penalty_t) :: gradient_jump_penalty
   contains
     procedure, pass(this) :: scheme_init => scalar_scheme_init
     procedure, pass(this) :: scheme_free => scalar_scheme_free
     procedure, pass(this) :: validate => scalar_scheme_validate
     procedure, pass(this) :: set_user_bc => scalar_scheme_set_user_bc
     procedure, pass(this) :: set_material_properties => &
          scalar_scheme_set_material_properties
     procedure, pass(this) :: update_material_properties => &
          scalar_scheme_update_material_properties
     procedure(scalar_scheme_init_intrf), pass(this), deferred :: init
     procedure(scalar_scheme_free_intrf), pass(this), deferred :: free
     procedure(scalar_scheme_step_intrf), pass(this), deferred :: step
     procedure(scalar_scheme_restart_intrf), pass(this), deferred :: restart
  end type scalar_scheme_t
  type, abstract :: scalar_scheme_t …
 
  abstract interface
     subroutine scalar_scheme_init_intrf(this, msh, coef, gs, params, user, &
          ulag, vlag, wlag, time_scheme, rho)
       import scalar_scheme_t
       import json_file
       import coef_t
       import gs_t
       import mesh_t
       import user_t
       import field_series_t
       import time_scheme_controller_t
       import rp
       class(scalar_scheme_t), target, intent(inout) :: this
       type(mesh_t), target, intent(inout) :: msh
       type(coef_t), target, intent(inout) :: coef
       type(gs_t), target, intent(inout) :: gs
       type(json_file), target, intent(inout) :: params
       type(user_t), target, intent(in) :: user
       type(field_series_t), target, intent(in) :: ulag, vlag, wlag
       type(time_scheme_controller_t), target, intent(in) :: time_scheme
       real(kind=rp), intent(in) :: rho
     subroutine scalar_scheme_init_intrf(this, msh, coef, gs, params, user, & …
     end subroutine scalar_scheme_init_intrf
  end interface
 
  abstract interface
     subroutine scalar_scheme_restart_intrf(this, dtlag, tlag)
       import scalar_scheme_t
       import chkp_t
       import rp
       class(scalar_scheme_t), target, intent(inout) :: this
       real(kind=rp) :: dtlag(10), tlag(10)
     subroutine scalar_scheme_restart_intrf(this, dtlag, tlag) …
     end subroutine scalar_scheme_restart_intrf
  end interface
 
  
  abstract interface
     subroutine scalar_scheme_free_intrf(this)
       import scalar_scheme_t
       class(scalar_scheme_t), intent(inout) :: this
     subroutine scalar_scheme_free_intrf(this) …
     end subroutine scalar_scheme_free_intrf
  end interface
 
  abstract interface
     subroutine scalar_scheme_step_intrf(this, t, tstep, dt, ext_bdf, &
          dt_controller)
       import scalar_scheme_t
       import time_scheme_controller_t
       import time_step_controller_t
       import rp
       class(scalar_scheme_t), intent(inout) :: this
       real(kind=rp), intent(inout) :: t
       integer, intent(inout) :: tstep
       real(kind=rp), intent(in) :: dt
       type(time_scheme_controller_t), intent(inout) :: ext_bdf
       type(time_step_controller_t), intent(in) :: dt_controller
     subroutine scalar_scheme_step_intrf(this, t, tstep, dt, ext_bdf, & …
     end subroutine scalar_scheme_step_intrf
  end interface
 
contains
 
  subroutine scalar_scheme_add_bcs(this, zones, bc_labels)
    class(scalar_scheme_t), intent(inout) :: this
    type(facet_zone_t), intent(inout) :: zones(NEKO_MSH_MAX_ZLBLS)
    character(len=NEKO_MSH_MAX_ZLBL_LEN), intent(in) :: bc_labels(:)
    character(len=NEKO_MSH_MAX_ZLBL_LEN) :: bc_label
    integer :: i
    real(kind=rp) :: dir_value, flux
    logical :: bc_exists
 
    do i = 1, size(bc_labels)
       bc_label = trim(bc_labels(i))
       if (bc_label(1:2) .eq. 'd=') then
! The idea of this commented piece of code is to merge bcs with the same
! Dirichlet value into 1 so that one has less kernel launches. Currently
! segfaults, needs investigation.
!          bc_exists = .false.
!          bc_idx = 0
!          do j = 1, i-1
!             if (bc_label .eq. bc_labels(j)) then
!                bc_exists = .true.
!                bc_idx = j
!             end if
!          end do
 
!          if (bc_exists) then
!             call this%dir_bcs(j)%mark_zone(zones(i))
!          else
          this%n_dir_bcs = this%n_dir_bcs + 1
          call this%dir_bcs(this%n_dir_bcs)%init_base(this%c_Xh)
          call this%dir_bcs(this%n_dir_bcs)%mark_zone(zones(i))
          read(bc_label(3:), *) dir_value
          call this%dir_bcs(this%n_dir_bcs)%set_g(dir_value)
          call this%dir_bcs(this%n_dir_bcs)%finalize()
       end if
 
       if (bc_label(1:2) .eq. 'n=') then
          this%n_neumann_bcs = this%n_neumann_bcs + 1
          call this%neumann_bcs(this%n_neumann_bcs)%init_base(this%c_Xh)
          call this%neumann_bcs(this%n_neumann_bcs)%mark_zone(zones(i))
          read(bc_label(3:), *) flux
          call this%neumann_bcs(this%n_neumann_bcs)%finalize_neumann(flux)
       end if
 
       if (bc_label(1:4) .eq. 'user') then
          call this%user_bc%mark_zone(zones(i))
       end if
 
    end do
 
    do i = 1, this%n_dir_bcs
       call bc_list_add(this%bclst_dirichlet, this%dir_bcs(i))
    end do
 
    ! Create list with just Neumann bcs
    call bc_list_init(this%bclst_neumann, this%n_neumann_bcs)
    do i = 1, this%n_neumann_bcs
       call bc_list_add(this%bclst_neumann, this%neumann_bcs(i))
    end do
 
  subroutine scalar_scheme_add_bcs(this, zones, bc_labels) …
  end subroutine scalar_scheme_add_bcs
 
  subroutine scalar_scheme_init(this, msh, c_Xh, gs_Xh, params, scheme, user, &
       rho)
    class(scalar_scheme_t), target, intent(inout) :: this
    type(mesh_t), target, intent(inout) :: msh
    type(coef_t), target, intent(inout) :: c_Xh
    type(gs_t), target, intent(inout) :: gs_Xh
    type(json_file), target, intent(inout) :: params
    character(len=*), intent(in) :: scheme
    type(user_t), target, intent(in) :: user
    real(kind=rp), intent(in) :: rho
    ! IO buffer for log output
    character(len=LOG_SIZE) :: log_buf
    ! Variables for retrieving json parameters
    logical :: logical_val
    real(kind=rp) :: real_val, solver_abstol
    integer :: integer_val, ierr
    character(len=:), allocatable :: solver_type, solver_precon
    real(kind=rp) :: gjp_param_a, gjp_param_b
 
    this%u => neko_field_registry%get_field('u')
    this%v => neko_field_registry%get_field('v')
    this%w => neko_field_registry%get_field('w')
 
    call neko_log%section('Scalar')
    call json_get(params, 'case.fluid.velocity_solver.type', solver_type)
    call json_get(params, 'case.fluid.velocity_solver.preconditioner', &
         solver_precon)
    call json_get(params, 'case.fluid.velocity_solver.absolute_tolerance', &
         solver_abstol)
 
    call json_get_or_default(params, &
         'case.fluid.velocity_solver.projection_space_size', &
         this%projection_dim, 20)
    call json_get_or_default(params, &
         'case.fluid.velocity_solver.projection_hold_steps', &
         this%projection_activ_step, 5)
 
 
    write(log_buf, '(A, A)') 'Type       : ', trim(scheme)
    call neko_log%message(log_buf)
    call neko_log%message('Ksp scalar : ('// trim(solver_type) // &
         ', ' // trim(solver_precon) // ')')
    write(log_buf, '(A,ES13.6)') ' `-abs tol :', solver_abstol
    call neko_log%message(log_buf)
 
    this%Xh => this%u%Xh
    this%dm_Xh => this%u%dof
    this%params => params
    this%msh => msh
    if (.not. neko_field_registry%field_exists('s')) then
       call neko_field_registry%add_field(this%dm_Xh, 's')
    end if
    this%s => neko_field_registry%get_field('s')
 
    call this%slag%init(this%s, 2)
 
    this%gs_Xh => gs_xh
    this%c_Xh => c_xh
 
    !
    ! Material properties
    !
    this%rho = rho
    call this%set_material_properties(params, user)
 
    write(log_buf, '(A,ES13.6)') 'rho        :', this%rho
    call neko_log%message(log_buf)
    write(log_buf, '(A,ES13.6)') 'lambda     :', this%lambda
    call neko_log%message(log_buf)
    write(log_buf, '(A,ES13.6)') 'cp         :', this%cp
    call neko_log%message(log_buf)
 
    !
    ! Turbulence modelling and variable material properties
    !
    if (params%valid_path('case.scalar.nut_field')) then
       call json_get(params, 'case.scalar.Pr_t', this%pr_turb)
       call json_get(params, 'case.scalar.nut_field', this%nut_field_name)
       this%variable_material_properties = .true.
    else
       this%nut_field_name = ""
    end if
 
    ! Fill lambda field with the physical value
    call this%lambda_field%init(this%dm_Xh, "lambda")
    if (neko_bcknd_device .eq. 1) then
       call device_cfill(this%lambda_field%x_d, this%lambda, &
            this%lambda_field%size())
    else
       call cfill(this%lambda_field%x, this%lambda, this%lambda_field%size())
    end if
 
    !
    ! Setup scalar boundary conditions
    !
    call bc_list_init(this%bclst_dirichlet)
    call this%user_bc%init_base(this%c_Xh)
 
    ! Read boundary types from the case file
    allocate(this%bc_labels(neko_msh_max_zlbls))
 
    ! A filler value
    this%bc_labels = "not"
 
    if (params%valid_path('case.scalar.boundary_types')) then
       call json_get(params, 'case.scalar.boundary_types', this%bc_labels, &
            'not')
    end if
 
    !
    ! Setup right-hand side field.
    !
    allocate(this%f_Xh)
    call this%f_Xh%init(this%dm_Xh, fld_name = "scalar_rhs")
 
    ! Initialize the source term
    call this%source_term%init(this%f_Xh, this%c_Xh, user)
    call this%source_term%add(params, 'case.scalar.source_terms')
 
    call scalar_scheme_add_bcs(this, msh%labeled_zones, this%bc_labels)
 
    ! Mark BC zones
    call this%user_bc%mark_zone(msh%wall)
    call this%user_bc%mark_zone(msh%inlet)
    call this%user_bc%mark_zone(msh%outlet)
    call this%user_bc%mark_zone(msh%outlet_normal)
    call this%user_bc%mark_zone(msh%sympln)
    call this%user_bc%finalize()
    if (this%user_bc%msk(0) .gt. 0) call bc_list_add(this%bclst_dirichlet, &
         this%user_bc)
 
    ! Add field dirichlet BCs
    call this%field_dir_bc%init_base(this%c_Xh)
    call this%field_dir_bc%mark_zones_from_list(msh%labeled_zones, &
         'd_s', this%bc_labels)
    call this%field_dir_bc%finalize()
    call mpi_allreduce(this%field_dir_bc%msk(0), integer_val, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    if (integer_val .gt. 0) call this%field_dir_bc%init_field('d_s')
 
    call bc_list_add(this%bclst_dirichlet, this%field_dir_bc)
 
    !
    ! Associate our field dirichlet update to the user one.
    !
    this%field_dir_bc%update => user%user_dirichlet_update
 
    call bc_list_init(this%field_dirichlet_bcs, size = 1)
    call bc_list_add(this%field_dirichlet_bcs, this%field_dir_bc)
 
 
    ! todo parameter file ksp tol should be added
    call json_get_or_default(params, &
         'case.fluid.velocity_solver.max_iterations', &
         integer_val, ksp_max_iter)
    call json_get_or_default(params, &
         'case.fluid.velocity_solver.monitor', &
         logical_val, .false.)
    call scalar_scheme_solver_factory(this%ksp, this%dm_Xh%size(), &
         solver_type, integer_val, solver_abstol, logical_val)
    call scalar_scheme_precon_factory(this%pc, this%ksp, &
                                      this%c_Xh, this%dm_Xh, this%gs_Xh, &
                                      this%bclst_dirichlet, solver_precon)
   
    ! Initiate gradient jump penalty
    call json_get_or_default(params, &
                            'case.scalar.gradient_jump_penalty.enabled',&
                            this%if_gradient_jump_penalty, .false.)
 
    if (this%if_gradient_jump_penalty .eqv. .true.) then
       if ((this%dm_Xh%xh%lx - 1) .eq. 1) then
          call json_get_or_default(params, &
                            'case.scalar.gradient_jump_penalty.tau',&
                            gjp_param_a, 0.02_rp)
          gjp_param_b = 0.0_rp
       else
          call json_get_or_default(params, &
                        'case.scalar.gradient_jump_penalty.scaling_factor',&
                            gjp_param_a, 0.8_rp)
          call json_get_or_default(params, &
                        'case.scalar.gradient_jump_penalty.scaling_exponent',&
                            gjp_param_b, 4.0_rp)
       end if
       call this%gradient_jump_penalty%init(params, this%dm_Xh, this%c_Xh, &
                                            gjp_param_a, gjp_param_b)
    end if
 
    call neko_log%end_section()
 
  subroutine scalar_scheme_init(this, msh, c_Xh, gs_Xh, params, scheme, user, & …
  end subroutine scalar_scheme_init
 
 
  subroutine scalar_scheme_free(this)
    class(scalar_scheme_t), intent(inout) :: this
 
    nullify(this%Xh)
    nullify(this%dm_Xh)
    nullify(this%gs_Xh)
    nullify(this%c_Xh)
    nullify(this%params)
 
    if (allocated(this%ksp)) then
       call krylov_solver_destroy(this%ksp)
       deallocate(this%ksp)
    end if
 
    if (allocated(this%pc)) then
       call precon_destroy(this%pc)
       deallocate(this%pc)
    end if
 
    if (allocated(this%bc_labels)) then
       deallocate(this%bc_labels)
    end if
 
    call this%source_term%free()
 
    call bc_list_free(this%bclst_dirichlet)
    call bc_list_free(this%bclst_neumann)
 
    call this%lambda_field%free()
    call this%slag%free()
 
    ! Free everything related to field dirichlet BCs
    call bc_list_free(this%field_dirichlet_bcs)
    call this%field_dir_bc%free()
 
    ! Free gradient jump penalty
    if (this%if_gradient_jump_penalty .eqv. .true.) then
       call this%gradient_jump_penalty%free()
    end if
 
  subroutine scalar_scheme_free(this) …
  end subroutine scalar_scheme_free
 
  subroutine scalar_scheme_validate(this)
    class(scalar_scheme_t), target, intent(inout) :: this
 
    if ( (.not. allocated(this%u%x)) .or. &
         (.not. allocated(this%v%x)) .or. &
         (.not. allocated(this%w%x)) .or. &
         (.not. allocated(this%s%x))) then
       call neko_error('Fields are not allocated')
    end if
 
    if (.not. allocated(this%ksp)) then
       call neko_error('No Krylov solver for velocity defined')
    end if
 
    if (.not. associated(this%Xh)) then
       call neko_error('No function space defined')
    end if
 
    if (.not. associated(this%dm_Xh)) then
       call neko_error('No dofmap defined')
    end if
 
    if (.not. associated(this%c_Xh)) then
       call neko_error('No coefficients defined')
    end if
 
    if (.not. associated(this%f_Xh)) then
       call neko_error('No rhs allocated')
    end if
 
    if (.not. associated(this%params)) then
       call neko_error('No parameters defined')
    end if
 
    !
    ! Setup checkpoint structure (if everything is fine)
    !
!    @todo no io for now
!    call this%chkp%init(this%u, this%v, this%w, this%p)
 
  subroutine scalar_scheme_validate(this) …
  end subroutine scalar_scheme_validate
 
  subroutine scalar_scheme_solver_factory(ksp, n, solver, max_iter, &
       abstol, monitor)
    class(ksp_t), allocatable, target, intent(inout) :: ksp
    integer, intent(in), value :: n
    integer, intent(in) :: max_iter
    character(len=*), intent(in) :: solver
    real(kind=rp) :: abstol
    logical, intent(in) :: monitor
 
    call krylov_solver_factory(ksp, n, solver, max_iter, &
         abstol, monitor = monitor)
 
  subroutine scalar_scheme_solver_factory(ksp, n, solver, max_iter, & …
  end subroutine scalar_scheme_solver_factory
 
  subroutine scalar_scheme_precon_factory(pc, ksp, coef, dof, gs, bclst, &
       pctype)
    class(pc_t), allocatable, target, intent(inout) :: pc
    class(ksp_t), target, intent(inout) :: ksp
    type(coef_t), target, intent(inout) :: coef
    type(dofmap_t), target, intent(inout) :: dof
    type(gs_t), target, intent(inout) :: gs
    type(bc_list_t), target, intent(inout) :: bclst
    character(len=*) :: pctype
 
    call precon_factory(pc, pctype)
 
    select type (pcp => pc)
      type is (jacobi_t)
       call pcp%init(coef, dof, gs)
      type is (sx_jacobi_t)
       call pcp%init(coef, dof, gs)
      type is (device_jacobi_t)
       call pcp%init(coef, dof, gs)
      type is (hsmg_t)
       if (len_trim(pctype) .gt. 4) then
          if (index(pctype, '+') .eq. 5) then
             call pcp%init(dof%msh, dof%Xh, coef, dof, gs, bclst, &
                  trim(pctype(6:)))
          else
             call neko_error('Unknown coarse grid solver')
          end if
       else
          call pcp%init(dof%msh, dof%Xh, coef, dof, gs, bclst)
       end if
    end select
 
    call ksp%set_pc(pc)
 
  subroutine scalar_scheme_precon_factory(pc, ksp, coef, dof, gs, bclst, & …
  end subroutine scalar_scheme_precon_factory
 
  subroutine scalar_scheme_set_user_bc(this, usr_eval)
    class(scalar_scheme_t), intent(inout) :: this
    procedure(usr_scalar_bc_eval) :: usr_eval
 
    call this%user_bc%set_eval(usr_eval)
 
  subroutine scalar_scheme_set_user_bc(this, usr_eval) …
  end subroutine scalar_scheme_set_user_bc
 
  subroutine scalar_scheme_update_material_properties(this)
    class(scalar_scheme_t), intent(inout) :: this
    type(field_t), pointer :: nut
    integer :: n
    ! Factor to transform nu_t to lambda_t
    real(kind=rp) :: lambda_factor
 
    lambda_factor = this%rho*this%cp/this%pr_turb
 
    if (this%variable_material_properties) then
       nut => neko_field_registry%get_field(this%nut_field_name)
       n = nut%size()
       if (neko_bcknd_device .eq. 1) then
          call device_cfill(this%lambda_field%x_d, this%lambda, n)
          call device_add2s2(this%lambda_field%x_d, nut%x_d, lambda_factor, n)
       else
          call cfill(this%lambda_field%x, this%lambda, n)
          call add2s2(this%lambda_field%x, nut%x, lambda_factor, n)
       end if
    end if
 
  subroutine scalar_scheme_update_material_properties(this) …
  end subroutine scalar_scheme_update_material_properties
 
  subroutine scalar_scheme_set_material_properties(this, params, user)
    class(scalar_scheme_t), intent(inout) :: this
    type(json_file), intent(inout) :: params
    type(user_t), target, intent(in) :: user
    character(len=LOG_SIZE) :: log_buf
    ! A local pointer that is needed to make Intel happy
    procedure(user_material_properties),  pointer :: dummy_mp_ptr
    real(kind=rp) :: dummy_mu, dummy_rho
 
    dummy_mp_ptr => dummy_user_material_properties
 
    if (.not. associated(user%material_properties, dummy_mp_ptr)) then
 
       write(log_buf, '(A)') "Material properties must be set in the user&
       & file!"
       call neko_log%message(log_buf)
       call user%material_properties(0.0_rp, 0, dummy_rho, dummy_mu, &
                                        this%cp, this%lambda, params)
    else
       if (params%valid_path('case.scalar.Pe') .and. &
           (params%valid_path('case.scalar.lambda') .or. &
            params%valid_path('case.scalar.cp'))) then
          call neko_error("To set the material properties for the scalar,&
          & either provide Pe OR lambda and cp in the case file.")
          ! Non-dimensional case
       else if (params%valid_path('case.scalar.Pe')) then
          write(log_buf, '(A)') 'Non-dimensional scalar material properties &
          & input.'
          call neko_log%message(log_buf, lvl = neko_log_verbose)
          write(log_buf, '(A)') 'Specific heat capacity will be set to 1,'
          call neko_log%message(log_buf, lvl = neko_log_verbose)
          write(log_buf, '(A)') 'conductivity to 1/Pe. Assumes density is 1.'
          call neko_log%message(log_buf, lvl = neko_log_verbose)
 
          ! Read Pe into lambda for further manipulation.
          call json_get(params, 'case.scalar.Pe', this%lambda)
          write(log_buf, '(A,ES13.6)') 'Pe         :',  this%lambda
          call neko_log%message(log_buf)
 
          ! Set cp and rho to 1 since the setup is non-dimensional.
          this%cp = 1.0_rp
          this%rho = 1.0_rp
          ! Invert the Pe to get conductivity
          this%lambda = 1.0_rp/this%lambda
          ! Dimensional case
       else
          call json_get(params, 'case.scalar.lambda', this%lambda)
          call json_get(params, 'case.scalar.cp', this%cp)
       end if
 
    end if
  subroutine scalar_scheme_set_material_properties(this, params, user) …
  end subroutine scalar_scheme_set_material_properties
 
 
 
end module scalar_scheme