fluid_scheme.f90

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module fluid_scheme
  use gather_scatter, only : gs_t
  use mean_sqr_flow, only : mean_sqr_flow_t
  use neko_config, only : neko_bcknd_device
  use checkpoint, only : chkp_t
  use mean_flow, only : mean_flow_t
  use num_types, only : rp
  use comm
  use fluid_source_term, only: fluid_source_term_t
  use field, only : field_t
  use space, only : space_t, gll
  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 wall, only : no_slip_wall_t
  use inflow, only : inflow_t
  use usr_inflow, only : usr_inflow_t, usr_inflow_eval
  use blasius, only : blasius_t
  use dirichlet, only : dirichlet_t
  use dong_outflow, only : dong_outflow_t
  use symmetry, only : symmetry_t
  use field_dirichlet, only : field_dirichlet_t
  use field_dirichlet_vector, only: field_dirichlet_vector_t
  use jacobi, only : jacobi_t
  use sx_jacobi, only : sx_jacobi_t
  use device_jacobi, only : device_jacobi_t
  use hsmg, only : hsmg_t
  use precon, only : pc_t, precon_factory, precon_destroy
  use fluid_stats, only : fluid_stats_t
  use bc, only : bc_t, bc_list_t, bc_list_init, bc_list_add, bc_list_free, &
       bc_list_apply_scalar, bc_list_apply_vector
  use mesh, only : mesh_t, neko_msh_max_zlbls, neko_msh_max_zlbl_len
  use math, only : cfill, add2s2
  use device_math, only : device_cfill, device_add2s2
  use time_scheme_controller, only : time_scheme_controller_t
  use operators, only : cfl
  use logger, only : neko_log, log_size, neko_log_verbose
  use field_registry, only : neko_field_registry
  use json_utils, only : json_get, json_get_or_default, json_extract_object
  use json_module, only : json_file
  use scratch_registry, only : scratch_registry_t
  use user_intf, only : user_t, dummy_user_material_properties, &
                        user_material_properties
  use utils, only : neko_error, neko_warning
  use field_series, only : field_series_t
  use time_step_controller, only : time_step_controller_t
  use field_math, only : field_cfill
  use wall_model_bc, only : wall_model_bc_t
  use shear_stress, only : shear_stress_t
  use gradient_jump_penalty, only : gradient_jump_penalty_t
  implicit none
  private
 
  type, abstract :: fluid_scheme_t
     type(field_t), pointer :: u => null() 
     type(field_t), pointer :: v => null() 
     type(field_t), pointer :: w => null() 
     type(field_t), pointer :: p => null() 
     type(field_series_t) :: ulag, vlag, wlag
     type(space_t) :: xh
     type(dofmap_t) :: dm_xh
     type(gs_t) :: gs_xh
     type(coef_t) :: c_xh
     type(fluid_source_term_t) :: source_term
     type(field_t), pointer :: f_x => null()
     type(field_t), pointer :: f_y => null()
     type(field_t), pointer :: f_z => null()
     class(ksp_t), allocatable :: ksp_vel
     class(ksp_t), allocatable :: ksp_prs
     class(pc_t), allocatable :: pc_vel
     class(pc_t), allocatable :: pc_prs
     integer :: vel_projection_dim
     integer :: pr_projection_dim
     integer :: vel_projection_activ_step
     integer :: pr_projection_activ_step
     type(no_slip_wall_t) :: bc_wall
     class(bc_t), allocatable :: bc_inflow
     type(wall_model_bc_t) :: bc_wallmodel
     logical :: if_gradient_jump_penalty
     type(gradient_jump_penalty_t) :: gradient_jump_penalty_u
     type(gradient_jump_penalty_t) :: gradient_jump_penalty_v
     type(gradient_jump_penalty_t) :: gradient_jump_penalty_w
 
     ! Attributes for field dirichlet BCs
     type(field_dirichlet_vector_t) :: user_field_bc_vel
     type(field_dirichlet_t) :: user_field_bc_prs
     type(dirichlet_t) :: bc_prs
     type(dong_outflow_t) :: bc_dong
     type(symmetry_t) :: bc_sym
     type(shear_stress_t) :: bc_sh
     type(bc_list_t) :: bclst_vel
     type(bc_list_t) :: bclst_vel_neumann
     type(bc_list_t) :: bclst_prs
     type(field_t) :: bdry
     type(json_file), pointer :: params
     type(mesh_t), pointer :: msh => null()    
     type(chkp_t) :: chkp
     type(mean_flow_t) :: mean
     type(fluid_stats_t) :: stats
     type(mean_sqr_flow_t) :: mean_sqr
     logical :: forced_flow_rate = .false.     
     logical :: freeze = .false.               
     real(kind=rp) :: mu
     type(field_t) :: mu_field
     character(len=:), allocatable :: nut_field_name
     logical :: variable_material_properties = .false.
     real(kind=rp) :: rho
     type(field_t) :: rho_field
     type(scratch_registry_t) :: scratch
     character(len=NEKO_MSH_MAX_ZLBL_LEN), allocatable :: bc_labels(:)
   contains
     procedure, pass(this) :: fluid_scheme_init_all
     procedure, pass(this) :: fluid_scheme_init_common
     generic :: scheme_init => fluid_scheme_init_all, fluid_scheme_init_common
     procedure, pass(this) :: scheme_free => fluid_scheme_free
     procedure, pass(this) :: validate => fluid_scheme_validate
     procedure, pass(this) :: bc_apply_vel => fluid_scheme_bc_apply_vel
     procedure, pass(this) :: bc_apply_prs => fluid_scheme_bc_apply_prs
     procedure, pass(this) :: set_usr_inflow => fluid_scheme_set_usr_inflow
     procedure, pass(this) :: compute_cfl => fluid_compute_cfl
     procedure, pass(this) :: set_material_properties => &
          fluid_scheme_set_material_properties
     procedure(fluid_scheme_init_intrf), pass(this), deferred :: init
     procedure(fluid_scheme_free_intrf), pass(this), deferred :: free
     procedure(fluid_scheme_step_intrf), pass(this), deferred :: step
     procedure(fluid_scheme_restart_intrf), pass(this), deferred :: restart
     procedure, private, pass(this) :: set_bc_type_output => &
       fluid_scheme_set_bc_type_output
     procedure, pass(this) :: update_material_properties => &
       fluid_scheme_update_material_properties
  end type fluid_scheme_t
  type, abstract :: fluid_scheme_t …
 
  abstract interface
     subroutine fluid_scheme_init_intrf(this, msh, lx, params, user, &
          time_scheme)
       import fluid_scheme_t
       import json_file
       import mesh_t
       import user_t
       import time_scheme_controller_t
       class(fluid_scheme_t), target, intent(inout) :: this
       type(mesh_t), target, intent(inout) :: msh
       integer, intent(inout) :: lx
       type(json_file), target, intent(inout) :: params
       type(user_t), target, intent(in) :: user
       type(time_scheme_controller_t), target, intent(in) :: time_scheme
     subroutine fluid_scheme_init_intrf(this, msh, lx, params, user, & …
     end subroutine fluid_scheme_init_intrf
  end interface
 
  abstract interface
     subroutine fluid_scheme_free_intrf(this)
       import fluid_scheme_t
       class(fluid_scheme_t), intent(inout) :: this
     subroutine fluid_scheme_free_intrf(this) …
     end subroutine fluid_scheme_free_intrf
  end interface
 
  abstract interface
     subroutine fluid_scheme_step_intrf(this, t, tstep, dt, ext_bdf, &
                                        dt_controller)
       import fluid_scheme_t
       import time_scheme_controller_t
       import time_step_controller_t
       import rp
       class(fluid_scheme_t), target, 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 fluid_scheme_step_intrf(this, t, tstep, dt, ext_bdf, & …
     end subroutine fluid_scheme_step_intrf
  end interface
 
  abstract interface
     subroutine fluid_scheme_restart_intrf(this, dtlag, tlag)
       import fluid_scheme_t
       import rp
       class(fluid_scheme_t), target, intent(inout) :: this
       real(kind=rp) :: dtlag(10), tlag(10)
 
     subroutine fluid_scheme_restart_intrf(this, dtlag, tlag) …
     end subroutine fluid_scheme_restart_intrf
  end interface
 
  interface
 
     module subroutine fluid_scheme_factory(object, type_name)
       class(fluid_scheme_t), intent(inout), allocatable :: object
       character(len=*) :: type_name
     end subroutine fluid_scheme_factory
  end interface
 
  public :: fluid_scheme_t, fluid_scheme_factory
 
contains
 
  subroutine fluid_scheme_init_common(this, msh, lx, params, scheme, user, &
      kspv_init)
    implicit none
    class(fluid_scheme_t), target, intent(inout) :: this
    type(mesh_t), target, intent(inout) :: msh
    integer, intent(inout) :: lx
    character(len=*), intent(in) :: scheme
    type(json_file), target, intent(inout) :: params
    type(user_t), target, intent(in) :: user
    logical, intent(in) :: kspv_init
    type(dirichlet_t) :: bdry_mask
    character(len=LOG_SIZE) :: log_buf
    real(kind=rp), allocatable :: real_vec(:)
    real(kind=rp) :: real_val, kappa, b, z0
    logical :: logical_val
    integer :: integer_val, ierr
    type(json_file) :: wm_json
    character(len=:), allocatable :: string_val1, string_val2
 
    !
    ! SEM simulation fundamentals
    !
 
    this%msh => msh
 
    if (msh%gdim .eq. 2) then
       call this%Xh%init(gll, lx, lx)
    else
       call this%Xh%init(gll, lx, lx, lx)
    end if
 
    call this%dm_Xh%init(msh, this%Xh)
 
    call this%gs_Xh%init(this%dm_Xh)
 
    call this%c_Xh%init(this%gs_Xh)
 
    ! Local scratch registry
    this%scratch = scratch_registry_t(this%dm_Xh, 10, 2)
 
    ! Case parameters
    this%params => params
 
 
    !
    ! First section of fluid log
    !
 
    call neko_log%section('Fluid')
    write(log_buf, '(A, A)') 'Type       : ', trim(scheme)
    call neko_log%message(log_buf)
 
    !
    ! Material properties
    !
    call this%set_material_properties(params, user)
 
    !
    ! Turbulence modelling and variable material properties
    !
    if (params%valid_path('case.fluid.nut_field')) then
       call json_get(params, 'case.fluid.nut_field', this%nut_field_name)
       this%variable_material_properties = .true.
    else
       this%nut_field_name = ""
    end if
 
    ! Fill mu and rho field with the physical value
 
    call this%mu_field%init(this%dm_Xh, "mu")
    call this%rho_field%init(this%dm_Xh, "mu")
    call field_cfill(this%mu_field, this%mu, this%mu_field%size())
    call field_cfill(this%rho_field, this%rho, this%mu_field%size())
 
    ! Since mu, rho is a field, and the none-stress simulation fetches
    ! data from the host arrays, we need to mirror the constant
    ! material properties on the host
    if (neko_bcknd_device .eq. 1) then
       call cfill(this%mu_field%x, this%mu, this%mu_field%size())
       call cfill(this%rho_field%x, this%rho, this%rho_field%size())
    end if
 
 
    ! Projection spaces
    call json_get_or_default(params, &
                        'case.fluid.velocity_solver.projection_space_size', &
                        this%vel_projection_dim, 20)
    call json_get_or_default(params, &
                        'case.fluid.pressure_solver.projection_space_size', &
                        this%pr_projection_dim, 20)
    call json_get_or_default(params, &
                        'case.fluid.velocity_solver.projection_hold_steps', &
                        this%vel_projection_activ_step, 5)
    call json_get_or_default(params, &
                        'case.fluid.pressure_solver.projection_hold_steps', &
                        this%pr_projection_activ_step, 5)
 
 
    call json_get_or_default(params, 'case.fluid.freeze', this%freeze, .false.)
 
    if (params%valid_path("case.fluid.flow_rate_force")) then
       this%forced_flow_rate = .true.
    end if
 
 
    if (lx .lt. 10) then
       write(log_buf, '(A, I1)') 'Poly order : ', lx-1
    else if (lx .ge. 10) then
       write(log_buf, '(A, I2)') 'Poly order : ', lx-1
    else
       write(log_buf, '(A, I3)') 'Poly order : ', lx-1
    end if
    call neko_log%message(log_buf)
    write(log_buf, '(A, I0)') 'DoFs       : ', this%dm_Xh%size()
    call neko_log%message(log_buf)
 
    write(log_buf, '(A,ES13.6)') 'rho        :',  this%rho
    call neko_log%message(log_buf)
    write(log_buf, '(A,ES13.6)') 'mu         :',  this%mu
    call neko_log%message(log_buf)
 
    call json_get(params, 'case.numerics.dealias', logical_val)
    write(log_buf, '(A, L1)') 'Dealias    : ',  logical_val
    call neko_log%message(log_buf)
 
    call json_get_or_default(params, 'case.output_boundary', logical_val, &
                             .false.)
    write(log_buf, '(A, L1)') 'Save bdry  : ',  logical_val
    call neko_log%message(log_buf)
    if (logical_val) then
       write(log_buf, '(A)') 'bdry keys: '
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'No-slip wall             ''w'' = 1'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Inlet/velocity dirichlet ''v'' = 2'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Outlet                   ''o'' = 3'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Symmetry               ''sym'' = 4'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Outlet-normal           ''on'' = 5'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Periodic                     = 6'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Dirichlet on velocity components: '
       call neko_log%message(log_buf)
       write(log_buf, '(A)') ' ''d_vel_u, d_vel_v, d_vel_w'' = 7'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Pressure dirichlet  ''d_pres'' = 8'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') '''d_vel_(u,v,w)'' and ''d_pres'' = 8'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Shear stress            ''sh'' = 9'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'Wall modelling          ''wm'' = 10'
       call neko_log%message(log_buf)
       write(log_buf, '(A)') 'No boundary condition set    = 0'
       call neko_log%message(log_buf)
    end if
 
 
    !
    ! Setup velocity boundary conditions
    !
    allocate(this%bc_labels(neko_msh_max_zlbls))
    this%bc_labels = "not"
 
    if (params%valid_path('case.fluid.boundary_types')) then
       call json_get(params, &
                     'case.fluid.boundary_types', &
                     this%bc_labels)
    end if
 
    call bc_list_init(this%bclst_vel)
 
    call this%bc_sym%init_base(this%c_Xh)
    call this%bc_sym%mark_zone(msh%sympln)
    call this%bc_sym%mark_zones_from_list(msh%labeled_zones, &
                        'sym', this%bc_labels)
    call this%bc_sym%finalize()
    call this%bc_sym%init(this%c_Xh)
    call bc_list_add(this%bclst_vel, this%bc_sym)
 
    ! Shear stress conditions
    call this%bc_sh%init_base(this%c_Xh)
    call this%bc_sh%mark_zones_from_list(msh%labeled_zones, &
                        'sh', this%bc_labels)
    call this%bc_sh%finalize()
      ! This marks the dirichlet and neumann conditions inside, and finalizes
      ! them.
    call this%bc_sh%init_shear_stress(this%c_Xh)
 
    call bc_list_add(this%bclst_vel, this%bc_sh%symmetry)
 
    ! Read stress value, default to [0 0 0]
    if (this%bc_sh%msk(0) .gt. 0) then
       call params%get('case.fluid.shear_stress.value', real_vec, logical_val)
       if (.not. logical_val .and. this%bc_sh%msk(0) .gt. 0) then
          call neko_warning("No stress values provided for sh boundaries, &
               & defaulting to 0. Use fluid.shear_stress.value to set.")
          allocate(real_vec(3))
          real_vec = 0.0_rp
       else if (size(real_vec) .ne. 3) then
          call neko_error ("The shear stress vector provided in &
               &fluid.shear_stress.value should have 3 components.")
       end if
       call this%bc_sh%set_stress(real_vec(1), real_vec(2), real_vec(3))
    end if
 
    call bc_list_init(this%bclst_vel_neumann)
    call bc_list_add(this%bclst_vel_neumann, this%bc_sh)
 
    !
    ! Inflow
    !
    if (params%valid_path('case.fluid.inflow_condition')) then
       call json_get(params, 'case.fluid.inflow_condition.type', string_val1)
       if (trim(string_val1) .eq. "uniform") then
          allocate(inflow_t::this%bc_inflow)
       else if (trim(string_val1) .eq. "blasius") then
          allocate(blasius_t::this%bc_inflow)
       else if (trim(string_val1) .eq. "user") then
          allocate(usr_inflow_t::this%bc_inflow)
       else
          call neko_error('Invalid inflow condition '//string_val1)
       end if
 
       call this%bc_inflow%init_base(this%c_Xh)
       call this%bc_inflow%mark_zone(msh%inlet)
       call this%bc_inflow%mark_zones_from_list(msh%labeled_zones, &
                        'v', this%bc_labels)
       call this%bc_inflow%finalize()
       call bc_list_add(this%bclst_vel, this%bc_inflow)
 
       if (trim(string_val1) .eq. "uniform") then
          call json_get(params, 'case.fluid.inflow_condition.value', real_vec)
          select type (bc_if => this%bc_inflow)
          type is (inflow_t)
             call bc_if%set_inflow(real_vec)
          end select
       else if (trim(string_val1) .eq. "blasius") then
          select type (bc_if => this%bc_inflow)
          type is (blasius_t)
             call json_get(params, 'case.fluid.blasius.delta', real_val)
             call json_get(params, 'case.fluid.blasius.approximation', &
                           string_val2)
             call json_get(params, 'case.fluid.blasius.freestream_velocity', &
                           real_vec)
 
             call bc_if%set_params(real_vec, real_val, string_val2)
 
          end select
       else if (trim(string_val1) .eq. "user") then
       end if
    end if
 
    !
    ! Wall models
    !
 
    call this%bc_wallmodel%init_base(this%c_Xh)
    call this%bc_wallmodel%mark_zones_from_list(msh%labeled_zones,&
         'wm', this%bc_labels)
    call this%bc_wallmodel%finalize()
 
    if (this%bc_wallmodel%msk(0) .gt. 0) then
       call json_extract_object(params, 'case.fluid.wall_modelling', wm_json)
       call this%bc_wallmodel%init_wall_model_bc(wm_json, this%mu / this%rho)
    else
       call this%bc_wallmodel%shear_stress_t%init_shear_stress(this%c_Xh) 
    end if
 
    call bc_list_add(this%bclst_vel, this%bc_wallmodel%symmetry)
    call bc_list_add(this%bclst_vel_neumann, this%bc_wallmodel)
 
    call this%bc_wall%init_base(this%c_Xh)
    call this%bc_wall%mark_zone(msh%wall)
    call this%bc_wall%mark_zones_from_list(msh%labeled_zones, &
                        'w', this%bc_labels)
    call this%bc_wall%finalize()
    call bc_list_add(this%bclst_vel, this%bc_wall)
 
    ! Setup field dirichlet bc for u-velocity
    call this%user_field_bc_vel%bc_u%init_base(this%c_Xh)
    call this%user_field_bc_vel%bc_u%mark_zones_from_list(msh%labeled_zones, &
                        'd_vel_u', this%bc_labels)
    call this%user_field_bc_vel%bc_u%finalize()
 
    call mpi_allreduce(this%user_field_bc_vel%bc_u%msk(0), integer_val, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    if (integer_val .gt. 0)  then
      call this%user_field_bc_vel%bc_u%init_field('d_vel_u')
    end if
 
    ! Setup field dirichlet bc for v-velocity
    call this%user_field_bc_vel%bc_v%init_base(this%c_Xh)
    call this%user_field_bc_vel%bc_v%mark_zones_from_list(msh%labeled_zones, &
                        'd_vel_v', this%bc_labels)
    call this%user_field_bc_vel%bc_v%finalize()
 
    call mpi_allreduce(this%user_field_bc_vel%bc_v%msk(0), integer_val, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    if (integer_val .gt. 0)  then
      call this%user_field_bc_vel%bc_v%init_field('d_vel_v')
    end if
 
    ! Setup field dirichlet bc for w-velocity
    call this%user_field_bc_vel%bc_w%init_base(this%c_Xh)
    call this%user_field_bc_vel%bc_w%mark_zones_from_list(msh%labeled_zones, &
                        'd_vel_w', this%bc_labels)
    call this%user_field_bc_vel%bc_w%finalize()
 
    call mpi_allreduce(this%user_field_bc_vel%bc_w%msk(0), integer_val, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    if (integer_val .gt. 0)  then
      call this%user_field_bc_vel%bc_w%init_field('d_vel_w')
    end if
 
    ! Setup our global field dirichlet bc
    call this%user_field_bc_vel%init_base(this%c_Xh)
    call this%user_field_bc_vel%mark_zones_from_list(msh%labeled_zones, &
                        'd_vel_u', this%bc_labels)
    call this%user_field_bc_vel%mark_zones_from_list(msh%labeled_zones, &
                        'd_vel_v', this%bc_labels)
    call this%user_field_bc_vel%mark_zones_from_list(msh%labeled_zones, &
                        'd_vel_w', this%bc_labels)
    call this%user_field_bc_vel%finalize()
 
    ! Add the field bc to velocity bcs
    call bc_list_add(this%bclst_vel, this%user_field_bc_vel)
 
    !
    ! Associate our field dirichlet update to the user one.
    !
    this%user_field_bc_vel%update => user%user_dirichlet_update
 
    !
    ! Initialize field list and bc list for user_dirichlet_update
    !
 
    ! Note, some of these are potentially not initialized !
    call this%user_field_bc_vel%field_list%init(4)
    call this%user_field_bc_vel%field_list%assign_to_field(1, &
            this%user_field_bc_vel%bc_u%field_bc)
    call this%user_field_bc_vel%field_list%assign_to_field(2, &
            this%user_field_bc_vel%bc_v%field_bc)
    call this%user_field_bc_vel%field_list%assign_to_field(3, &
            this%user_field_bc_vel%bc_w%field_bc)
    call this%user_field_bc_vel%field_list%assign_to_field(4, &
            this%user_field_bc_prs%field_bc)
 
    call bc_list_init(this%user_field_bc_vel%bc_list, size = 4)
    ! Note, bc_list_add only adds if the bc is not empty
    call bc_list_add(this%user_field_bc_vel%bc_list, &
                     this%user_field_bc_vel%bc_u)
    call bc_list_add(this%user_field_bc_vel%bc_list, &
                     this%user_field_bc_vel%bc_v)
    call bc_list_add(this%user_field_bc_vel%bc_list, &
                     this%user_field_bc_vel%bc_w)
 
    !
    ! Check if we need to output boundary types to a separate field
    call fluid_scheme_set_bc_type_output(this, params)
 
    !
    ! Setup right-hand side fields.
    !
    allocate(this%f_x)
    allocate(this%f_y)
    allocate(this%f_z)
    call this%f_x%init(this%dm_Xh, fld_name = "fluid_rhs_x")
    call this%f_y%init(this%dm_Xh, fld_name = "fluid_rhs_y")
    call this%f_z%init(this%dm_Xh, fld_name = "fluid_rhs_z")
 
    ! Initialize the source term
    call this%source_term%init(this%f_x, this%f_y, this%f_z, this%c_Xh, user)
    call this%source_term%add(params, 'case.fluid.source_terms')
 
    ! If case.output_boundary is true, set the values for the bc types in the
    ! output of the field.
    call this%set_bc_type_output(params)
 
    ! Initialize velocity solver
    if (kspv_init) then
       call neko_log%section("Velocity solver")
       call json_get_or_default(params, &
                                'case.fluid.velocity_solver.max_iterations', &
                                integer_val, ksp_max_iter)
       call json_get(params, 'case.fluid.velocity_solver.type', string_val1)
       call json_get(params, 'case.fluid.velocity_solver.preconditioner', &
                     string_val2)
       call json_get(params, 'case.fluid.velocity_solver.absolute_tolerance', &
                     real_val)
       call json_get_or_default(params, &
                                'case.fluid.velocity_solver.monitor', &
                                logical_val, .false.)
 
       call neko_log%message('Type       : ('// trim(string_val1) // &
           ', ' // trim(string_val2) // ')')
 
       write(log_buf, '(A,ES13.6)') 'Abs tol    :',  real_val
       call neko_log%message(log_buf)
       call fluid_scheme_solver_factory(this%ksp_vel, this%dm_Xh%size(), &
            string_val1, integer_val, real_val, logical_val)
       call fluid_scheme_precon_factory(this%pc_vel, this%ksp_vel, &
            this%c_Xh, this%dm_Xh, this%gs_Xh, this%bclst_vel, string_val2)
       call neko_log%end_section()
    end if
 
    ! Assign velocity fields
    call neko_field_registry%add_field(this%dm_Xh, 'u')
    call neko_field_registry%add_field(this%dm_Xh, 'v')
    call neko_field_registry%add_field(this%dm_Xh, 'w')
    this%u => neko_field_registry%get_field('u')
    this%v => neko_field_registry%get_field('v')
    this%w => neko_field_registry%get_field('w')
 
    !! Initialize time-lag fields
    call this%ulag%init(this%u, 2)
    call this%vlag%init(this%v, 2)
    call this%wlag%init(this%w, 2)
 
 
  subroutine fluid_scheme_init_common(this, msh, lx, params, scheme, user, & …
  end subroutine fluid_scheme_init_common
 
  subroutine fluid_scheme_init_all(this, msh, lx, params, kspv_init, &
       kspp_init, scheme, user)
    implicit none
    class(fluid_scheme_t), target, intent(inout) :: this
    type(mesh_t), target, intent(inout) :: msh
    integer, intent(inout) :: lx
    type(json_file), target, intent(inout) :: params
    type(user_t), target, intent(in) :: user
    logical :: kspv_init
    logical :: kspp_init
    character(len=*), intent(in) :: scheme
    real(kind=rp) :: abs_tol
    integer :: integer_val, ierr
    logical :: logical_val
    character(len=:), allocatable :: solver_type, precon_type
    character(len=LOG_SIZE) :: log_buf
    real(kind=rp) :: gjp_param_a, gjp_param_b
 
    call fluid_scheme_init_common(this, msh, lx, params, scheme, user, &
         kspv_init)
 
    call neko_field_registry%add_field(this%dm_Xh, 'p')
    this%p => neko_field_registry%get_field('p')
 
    !
    ! Setup pressure boundary conditions
    !
    call bc_list_init(this%bclst_prs)
    call this%bc_prs%init_base(this%c_Xh)
    call this%bc_prs%mark_zones_from_list(msh%labeled_zones, &
                        'o', this%bc_labels)
    call this%bc_prs%mark_zones_from_list(msh%labeled_zones, &
                        'on', this%bc_labels)
 
    ! Field dirichlet pressure bc
    call this%user_field_bc_prs%init_base(this%c_Xh)
    call this%user_field_bc_prs%mark_zones_from_list(msh%labeled_zones, &
                        'd_pres', this%bc_labels)
    call this%user_field_bc_prs%finalize()
    call mpi_allreduce(this%user_field_bc_prs%msk(0), integer_val, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
 
    if (integer_val .gt. 0) call this%user_field_bc_prs%init_field('d_pres')
    call bc_list_add(this%bclst_prs, this%user_field_bc_prs)
    call bc_list_add(this%user_field_bc_vel%bc_list, this%user_field_bc_prs)
 
    if (msh%outlet%size .gt. 0) then
       call this%bc_prs%mark_zone(msh%outlet)
    end if
    if (msh%outlet_normal%size .gt. 0) then
       call this%bc_prs%mark_zone(msh%outlet_normal)
    end if
 
    call this%bc_prs%finalize()
    call this%bc_prs%set_g(0.0_rp)
    call bc_list_add(this%bclst_prs, this%bc_prs)
    call this%bc_dong%init_base(this%c_Xh)
    call this%bc_dong%mark_zones_from_list(msh%labeled_zones, &
                        'o+dong', this%bc_labels)
    call this%bc_dong%mark_zones_from_list(msh%labeled_zones, &
                        'on+dong', this%bc_labels)
    call this%bc_dong%finalize()
 
 
    call this%bc_dong%init(this%c_Xh, params)
 
    call bc_list_add(this%bclst_prs, this%bc_dong)
 
    ! Pressure solver
    if (kspp_init) then
       call neko_log%section("Pressure solver")
 
       call json_get_or_default(params, &
                               'case.fluid.pressure_solver.max_iterations', &
                               integer_val, ksp_max_iter)
       call json_get(params, 'case.fluid.pressure_solver.type', solver_type)
       call json_get(params, 'case.fluid.pressure_solver.preconditioner', &
                     precon_type)
       call json_get(params, 'case.fluid.pressure_solver.absolute_tolerance', &
                     abs_tol)
       call json_get_or_default(params, &
                                'case.fluid.pressure_solver.monitor', &
                                logical_val, .false.)
       call neko_log%message('Type       : ('// trim(solver_type) // &
             ', ' // trim(precon_type) // ')')
       write(log_buf, '(A,ES13.6)') 'Abs tol    :',  abs_tol
       call neko_log%message(log_buf)
 
       call fluid_scheme_solver_factory(this%ksp_prs, this%dm_Xh%size(), &
            solver_type, integer_val, abs_tol, logical_val)
       call fluid_scheme_precon_factory(this%pc_prs, this%ksp_prs, &
            this%c_Xh, this%dm_Xh, this%gs_Xh, this%bclst_prs, precon_type)
 
       call neko_log%end_section()
 
    end if
 
    ! Initiate gradient jump penalty
    call json_get_or_default(params, &
                            'case.fluid.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.fluid.gradient_jump_penalty.tau',&
                            gjp_param_a, 0.02_rp)
          gjp_param_b = 0.0_rp
       else
          call json_get_or_default(params, &
                        'case.fluid.gradient_jump_penalty.scaling_factor',&
                            gjp_param_a, 0.8_rp)
          call json_get_or_default(params, &
                        'case.fluid.gradient_jump_penalty.scaling_exponent',&
                            gjp_param_b, 4.0_rp)
       end if
       call this%gradient_jump_penalty_u%init(params, this%dm_Xh, this%c_Xh, &
                                              gjp_param_a, gjp_param_b)
       call this%gradient_jump_penalty_v%init(params, this%dm_Xh, this%c_Xh, &
                                              gjp_param_a, gjp_param_b)
       call this%gradient_jump_penalty_w%init(params, this%dm_Xh, this%c_Xh, &
                                              gjp_param_a, gjp_param_b)
    end if
 
    call neko_log%end_section()
 
  subroutine fluid_scheme_init_all(this, msh, lx, params, kspv_init, & …
  end subroutine fluid_scheme_init_all
 
  subroutine fluid_scheme_free(this)
    class(fluid_scheme_t), intent(inout) :: this
 
    call this%bdry%free()
 
    if (allocated(this%bc_inflow)) then
       call this%bc_inflow%free()
    end if
 
    call this%bc_wall%free()
    call this%bc_sym%free()
    call this%bc_sh%free()
 
    !
    ! Free everything related to field_dirichlet BCs
    !
    call this%user_field_bc_prs%field_bc%free()
    call this%user_field_bc_prs%free()
    call this%user_field_bc_vel%bc_u%field_bc%free()
    call this%user_field_bc_vel%bc_v%field_bc%free()
    call this%user_field_bc_vel%bc_w%field_bc%free()
    call this%user_field_bc_vel%free()
 
    call this%Xh%free()
 
    if (allocated(this%ksp_vel)) then
       call krylov_solver_destroy(this%ksp_vel)
       deallocate(this%ksp_vel)
    end if
 
    if (allocated(this%ksp_prs)) then
       call krylov_solver_destroy(this%ksp_prs)
       deallocate(this%ksp_prs)
    end if
 
    if (allocated(this%pc_vel)) then
       call precon_destroy(this%pc_vel)
       deallocate(this%pc_vel)
    end if
 
    if (allocated(this%pc_prs)) then
       call precon_destroy(this%pc_prs)
       deallocate(this%pc_prs)
    end if
 
    if (allocated(this%bc_labels)) then
       deallocate(this%bc_labels)
    end if
 
    call this%source_term%free()
 
    call this%gs_Xh%free()
 
    call this%c_Xh%free()
 
    call bc_list_free(this%bclst_vel)
 
    call this%scratch%free()
 
    nullify(this%params)
 
    nullify(this%u)
    nullify(this%v)
    nullify(this%w)
    nullify(this%p)
 
    call this%ulag%free()
    call this%vlag%free()
    call this%wlag%free()
 
 
    if (associated(this%f_x)) then
       call this%f_x%free()
    end if
 
    if (associated(this%f_y)) then
       call this%f_y%free()
    end if
 
    if (associated(this%f_z)) then
       call this%f_z%free()
    end if
 
    nullify(this%f_x)
    nullify(this%f_y)
    nullify(this%f_z)
 
    call this%mu_field%free()
 
    ! Free gradient jump penalty
    if (this%if_gradient_jump_penalty .eqv. .true.) then
       call this%gradient_jump_penalty_u%free()
       call this%gradient_jump_penalty_v%free()
       call this%gradient_jump_penalty_w%free()
    end if
 
 
  subroutine fluid_scheme_free(this) …
  end subroutine fluid_scheme_free
 
  subroutine fluid_scheme_validate(this)
    class(fluid_scheme_t), target, intent(inout) :: this
    ! Variables for retrieving json parameters
    logical :: logical_val
 
    if ( (.not. associated(this%u)) .or. &
         (.not. associated(this%v)) .or. &
         (.not. associated(this%w)) .or. &
         (.not. associated(this%p))) then
       call neko_error('Fields are not registered')
    end if
 
    if ( (.not. allocated(this%u%x)) .or. &
         (.not. allocated(this%v%x)) .or. &
         (.not. allocated(this%w%x)) .or. &
         (.not. allocated(this%p%x))) then
       call neko_error('Fields are not allocated')
    end if
 
    if (.not. allocated(this%ksp_vel)) then
       call neko_error('No Krylov solver for velocity defined')
    end if
 
    if (.not. allocated(this%ksp_prs)) then
       call neko_error('No Krylov solver for pressure defined')
    end if
 
    if (.not. associated(this%params)) then
       call neko_error('No parameters defined')
    end if
 
    if (allocated(this%bc_inflow)) then
       select type (ip => this%bc_inflow)
       type is (usr_inflow_t)
          call ip%validate
       end select
    end if
 
    !
    ! Setup checkpoint structure (if everything is fine)
    !
    call this%chkp%init(this%u, this%v, this%w, this%p)
 
  subroutine fluid_scheme_validate(this) …
  end subroutine fluid_scheme_validate
 
  subroutine fluid_scheme_bc_apply_vel(this, t, tstep)
    class(fluid_scheme_t), intent(inout) :: this
    real(kind=rp), intent(in) :: t
    integer, intent(in) :: tstep
 
    call bc_list_apply_vector(this%bclst_vel, &
         this%u%x, this%v%x, this%w%x, this%dm_Xh%size(), t, tstep)
 
  subroutine fluid_scheme_bc_apply_vel(this, t, tstep) …
  end subroutine fluid_scheme_bc_apply_vel
 
  subroutine fluid_scheme_bc_apply_prs(this, t, tstep)
    class(fluid_scheme_t), intent(inout) :: this
    real(kind=rp), intent(in) :: t
    integer, intent(in) :: tstep
 
    call bc_list_apply_scalar(this%bclst_prs, this%p%x, &
                              this%p%dof%size(), t, tstep)
 
  subroutine fluid_scheme_bc_apply_prs(this, t, tstep) …
  end subroutine fluid_scheme_bc_apply_prs
 
  subroutine fluid_scheme_solver_factory(ksp, n, solver, &
                                         max_iter, abstol, monitor)
    class(ksp_t), allocatable, target, intent(inout) :: ksp
    integer, intent(in), value :: n
    character(len=*), intent(in) :: solver
    integer, intent(in) :: max_iter
    real(kind=rp), intent(in) :: abstol
    logical, intent(in) :: monitor
 
    call krylov_solver_factory(ksp, n, solver, max_iter, abstol, &
                               monitor = monitor)
 
  subroutine fluid_scheme_solver_factory(ksp, n, solver, & …
  end subroutine fluid_scheme_solver_factory
 
  subroutine fluid_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 fluid_scheme_precon_factory(pc, ksp, coef, dof, gs, bclst, & …
  end subroutine fluid_scheme_precon_factory
 
  subroutine fluid_scheme_set_usr_inflow(this, usr_eval)
    class(fluid_scheme_t), intent(inout) :: this
    procedure(usr_inflow_eval) :: usr_eval
 
    select type (bc_if => this%bc_inflow)
    type is (usr_inflow_t)
       call bc_if%set_eval(usr_eval)
    class default
       call neko_error("Not a user defined inflow condition")
    end select
  subroutine fluid_scheme_set_usr_inflow(this, usr_eval) …
  end subroutine fluid_scheme_set_usr_inflow
 
  function fluid_compute_cfl(this, dt) result(c)
    class(fluid_scheme_t), intent(in) :: this
    real(kind=rp), intent(in) :: dt
    real(kind=rp) :: c
 
    c = cfl(dt, this%u%x, this%v%x, this%w%x, &
         this%Xh, this%c_Xh, this%msh%nelv, this%msh%gdim)
 
  function fluid_compute_cfl(this, dt) result(c) …
  end function fluid_compute_cfl
 
  subroutine fluid_scheme_set_bc_type_output(this, params)
    class(fluid_scheme_t), target, intent(inout) :: this
    type(json_file), intent(inout) :: params
    type(dirichlet_t) :: bdry_mask
    logical :: found
 
    !
    ! Check if we need to output boundaries
    !
    call json_get_or_default(params, 'case.output_boundary', found, .false.)
 
    if (found) then
      call this%bdry%init(this%dm_Xh, 'bdry')
      this%bdry = 0.0_rp
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zone(this%msh%wall)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'w', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(1.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zone(this%msh%inlet)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'v', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(2.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zone(this%msh%outlet)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'o', this%bc_labels)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'o+dong', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(3.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zone(this%msh%sympln)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'sym', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(4.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zone(this%msh%outlet_normal)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'on', this%bc_labels)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'on+dong', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(5.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zone(this%msh%periodic)
      call bdry_mask%finalize()
      call bdry_mask%set_g(6.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'd_vel_u', this%bc_labels)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'd_vel_v', this%bc_labels)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'd_vel_w', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(7.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'd_pres', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(8.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'sh', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(9.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
      call bdry_mask%init_base(this%c_Xh)
      call bdry_mask%mark_zones_from_list(this%msh%labeled_zones, &
                     'wm', this%bc_labels)
      call bdry_mask%finalize()
      call bdry_mask%set_g(10.0_rp)
      call bdry_mask%apply_scalar(this%bdry%x, this%dm_Xh%size())
      call bdry_mask%free()
 
    end if
 
  subroutine fluid_scheme_set_bc_type_output(this, params) …
  end subroutine fluid_scheme_set_bc_type_output
 
  subroutine fluid_scheme_update_material_properties(this)
    class(fluid_scheme_t), intent(inout) :: this
    type(field_t), pointer :: nut
    integer :: n
 
    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%mu_field%x_d, this%mu, n)
         call device_add2s2(this%mu_field%x_d, nut%x_d, this%rho, n)
      else
         call cfill(this%mu_field%x, this%mu, n)
         call add2s2(this%mu_field%x, nut%x, this%rho, n)
      end if
    end if
 
  subroutine fluid_scheme_update_material_properties(this) …
  end subroutine fluid_scheme_update_material_properties
 
  subroutine fluid_scheme_set_material_properties(this, params, user)
    class(fluid_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
    logical :: nondimensional
    real(kind=rp) :: dummy_lambda, dummy_cp
 
    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, this%rho, this%mu, &
            dummy_cp, dummy_lambda, params)
    else
       ! Incorrect user input
       if (params%valid_path('case.fluid.Re') .and. &
           (params%valid_path('case.fluid.mu') .or. &
            params%valid_path('case.fluid.rho'))) then
          call neko_error("To set the material properties for the fluid,&
          & either provide Re OR mu and rho in the case file.")
 
          ! Non-dimensional case
       else if (params%valid_path('case.fluid.Re')) then
 
          write(log_buf, '(A)') 'Non-dimensional fluid material properties &
          & input.'
          call neko_log%message(log_buf, lvl = neko_log_verbose)
          write(log_buf, '(A)') 'Density will be set to 1, dynamic viscosity to&
          & 1/Re.'
          call neko_log%message(log_buf, lvl = neko_log_verbose)
 
          ! Read Re into mu for further manipulation.
          call json_get(params, 'case.fluid.Re', this%mu)
          write(log_buf, '(A)') 'Read non-dimensional material properties'
          call neko_log%message(log_buf)
          write(log_buf, '(A,ES13.6)') 'Re         :',  this%mu
          call neko_log%message(log_buf)
 
          ! Set rho to 1 since the setup is non-dimensional.
          this%rho = 1.0_rp
          ! Invert the Re to get viscosity.
          this%mu = 1.0_rp/this%mu
          ! Dimensional case
       else
          call json_get(params, 'case.fluid.mu', this%mu)
          call json_get(params, 'case.fluid.rho', this%rho)
       end if
 
    end if
  subroutine fluid_scheme_set_material_properties(this, params, user) …
  end subroutine fluid_scheme_set_material_properties
 
end module fluid_scheme