fluid_scheme_incompressible.f90

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module fluid_scheme_incompressible
  use fluid_scheme_base, only : fluid_scheme_base_t
  use gather_scatter, only : gs_t, gs_op_min, gs_op_max
  use neko_config, only : neko_bcknd_device
  use checkpoint, only : chkp_t
  use num_types, only : rp, i8
  use fluid_source_term, only : fluid_source_term_t
  use field, only : field_t
  use space, only : gll
  use dofmap, only : dofmap_t
  use krylov, only : ksp_t, krylov_solver_factory, ksp_max_iter
  use coefs, only : coef_t
  use dirichlet, only : dirichlet_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 phmg, only : phmg_t
  use precon, only : pc_t, precon_factory, precon_destroy
  use fluid_stats, only : fluid_stats_t
  use bc, only : bc_t
  use bc_list, only : bc_list_t
  use mesh, only : mesh_t
  use math, only : glsum
  use operators, only : cfl, rotate_cyc
  use logger, only : neko_log, log_size, neko_log_verbose
  use registry, only : neko_registry
  use json_utils, only : json_get, json_get_or_default, json_get_or_lookup, &
       json_get_or_lookup_or_default
  use json_module, only : json_file
  use scratch_registry, only : neko_scratch_registry
  use user_intf, only : user_t, dummy_user_material_properties, &
       user_material_properties_intf
  use utils, only : neko_error
  use field_math, only : field_cfill, field_addcol3, field_copy
  use device, only : device_event_sync, glb_cmd_event, device_to_host, &
       device_memcpy
  use time_state, only : time_state_t
  implicit none
  private
 
  type, abstract, extends(fluid_scheme_base_t) :: fluid_scheme_incompressible_t
     type(fluid_source_term_t) :: source_term
     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
     logical :: strict_convergence
     logical :: allow_stabilization
     type(field_t), pointer :: u_e => null() 
     type(field_t), pointer :: v_e => null() 
     type(field_t), pointer :: w_e => null() 
 
     type(fluid_stats_t) :: stats
     logical :: forced_flow_rate = .false. 
 
     character(len=:), allocatable :: nut_field_name
 
     ! The total viscosity field
     type(field_t), pointer :: mu_tot => null()
 
     integer(kind=i8) :: glb_n_points
     integer(kind=i8) :: glb_unique_points
   contains
     procedure, pass(this) :: init_base => fluid_scheme_init_base
     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) :: compute_cfl => fluid_compute_cfl
     procedure, pass(this) :: set_material_properties => &
          fluid_scheme_set_material_properties
 
     procedure, pass(this) :: update_material_properties => &
          fluid_scheme_update_material_properties
     procedure, nopass :: solver_factory => fluid_scheme_solver_factory
     procedure, pass(this) :: precon_factory_ => fluid_scheme_precon_factory
  end type fluid_scheme_incompressible_t
 
  interface
 
     module subroutine fluid_scheme_factory(object, type_name)
       class(fluid_scheme_base_t), intent(inout), allocatable :: object
       character(len=*) :: type_name
     end subroutine fluid_scheme_factory
  end interface
 
  public :: fluid_scheme_incompressible_t, fluid_scheme_factory
 
contains
 
  subroutine fluid_scheme_init_base(this, msh, lx, params, scheme, user, &
       kspv_init)
    implicit none
    class(fluid_scheme_incompressible_t), target, intent(inout) :: this
    type(mesh_t), target, intent(inout) :: msh
    integer, intent(in) :: 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
    type(json_file) :: json_subdict
 
    !
    ! 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)
 
    ! Assign Dofmap to scratch registry
    call neko_scratch_registry%set_dofmap(this%dm_Xh)
 
    ! Assign a name
    call json_get_or_default(params, 'case.fluid.name', this%name, "fluid")
 
    !
    ! First section of fluid log
    !
 
    call neko_log%section('Fluid')
    write(log_buf, '(A, A)') 'Type       : ', trim(scheme)
    call neko_log%message(log_buf)
    write(log_buf, '(A, A)') 'Name       : ', trim(this%name)
    call neko_log%message(log_buf)
 
    ! Assign velocity fields
    call neko_registry%add_field(this%dm_Xh, 'u')
    call neko_registry%add_field(this%dm_Xh, 'v')
    call neko_registry%add_field(this%dm_Xh, 'w')
    this%u => neko_registry%get_field('u')
    this%v => neko_registry%get_field('v')
    this%w => neko_registry%get_field('w')
 
    !
    ! Material properties
    !
    call this%set_material_properties(params, user)
 
    ! Projection spaces
    call json_get_or_lookup_or_default(params, &
         'case.fluid.velocity_solver.projection_space_size', &
         this%vel_projection_dim, 0)
    call json_get_or_lookup_or_default(params, &
         'case.fluid.pressure_solver.projection_space_size', &
         this%pr_projection_dim, 0)
    call json_get_or_lookup_or_default(params, &
         'case.fluid.velocity_solver.projection_hold_steps', &
         this%vel_projection_activ_step, 5)
    call json_get_or_lookup_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)
    this%glb_n_points = int(this%msh%glb_nelv, i8)*int(this%Xh%lxyz, i8)
    this%glb_unique_points = int(glsum(this%c_Xh%mult, this%dm_Xh%size()), i8)
 
    write(log_buf, '(A, I0)') 'GLL points : ', this%glb_n_points
    call neko_log%message(log_buf)
    write(log_buf, '(A, I0)') 'Unique pts.: ', this%glb_unique_points
    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)
 
    call json_get_or_default(params, "case.fluid.full_stress_formulation", &
         logical_val, .false.)
    write(log_buf, '(A, L1)') 'Full stress: ', logical_val
    call neko_log%message(log_buf)
 
 
    !
    ! 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 velocity solver
    if (kspv_init) then
       call neko_log%section("Velocity solver")
       call json_get_or_lookup_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.type', &
            string_val2)
       call json_get(params, &
            'case.fluid.velocity_solver.preconditioner', json_subdict)
       call json_get_or_lookup(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 this%solver_factory(this%ksp_vel, this%dm_Xh%size(), &
            string_val1, integer_val, real_val, logical_val)
       call this%precon_factory_(this%pc_vel, this%ksp_vel, &
            this%c_Xh, this%dm_Xh, this%gs_Xh, this%bcs_vel, &
            string_val2, json_subdict)
       call neko_log%end_section()
    end if
 
    ! Strict convergence for the velocity solver
    call json_get_or_default(params, 'case.fluid.strict_convergence', &
         this%strict_convergence, .false.)
    ! Allow stabilization period where we do not warn about non-convergence
    call json_get_or_default(params, 'case.fluid.allow_stabilization', &
         this%allow_stabilization, .false.)
 
 
    !! 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)
 
    call neko_registry%add_field(this%dm_Xh, 'u_e')
    call neko_registry%add_field(this%dm_Xh, 'v_e')
    call neko_registry%add_field(this%dm_Xh, 'w_e')
    this%u_e => neko_registry%get_field('u_e')
    this%v_e => neko_registry%get_field('v_e')
    this%w_e => neko_registry%get_field('w_e')
 
    ! Initialize the source term
    call neko_log%section('Fluid Source term')
    call this%source_term%init(this%f_x, this%f_y, this%f_z, this%c_Xh, user, &
         this%name)
    call this%source_term%add(params, 'case.fluid.source_terms')
    call neko_log%end_section()
 
  end subroutine fluid_scheme_init_base
 
  subroutine fluid_scheme_free(this)
    class(fluid_scheme_incompressible_t), intent(inout) :: this
    class(bc_t), pointer :: bc
    integer :: i
 
 
    call this%Xh%free()
 
    if (allocated(this%ksp_vel)) then
       call this%ksp_vel%free()
       deallocate(this%ksp_vel)
    end if
 
    if (allocated(this%ksp_prs)) then
       call this%ksp_prs%free()
       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
 
    do i = 1, this%bcs_vel%size()
       bc => this%bcs_vel%get(i)
       call bc%free()
    end do
    call this%bcs_vel%free()
 
    do i = 1, this%bcs_prs%size()
       bc => this%bcs_prs%get(i)
       call bc%free()
    end do
    call this%bcs_prs%free()
 
    call this%source_term%free()
 
    call this%gs_Xh%free()
 
    call this%c_Xh%free()
 
    nullify(this%u)
    nullify(this%v)
    nullify(this%w)
    nullify(this%p)
 
    nullify(this%u_e)
    nullify(this%v_e)
    nullify(this%w_e)
 
    call this%ulag%free()
    call this%vlag%free()
    call this%wlag%free()
 
 
    if (associated(this%f_x)) then
       call this%f_x%free()
       deallocate(this%f_x)
    end if
 
    if (associated(this%f_y)) then
       call this%f_y%free()
       deallocate(this%f_y)
    end if
 
    if (associated(this%f_z)) then
       call this%f_z%free()
       deallocate(this%f_z)
    end if
 
    nullify(this%f_x)
    nullify(this%f_y)
    nullify(this%f_z)
    nullify(this%rho)
    nullify(this%mu)
    nullify(this%mu_tot)
 
    call this%dm_Xh%free()
    call this%Xh%free()
    nullify(this%msh)
 
  end subroutine fluid_scheme_free
 
  subroutine fluid_scheme_validate(this)
    class(fluid_scheme_incompressible_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
 
  end subroutine fluid_scheme_validate
 
  subroutine fluid_scheme_bc_apply_vel(this, time, strong)
    class(fluid_scheme_incompressible_t), intent(inout) :: this
    type(time_state_t), intent(in) :: time
    logical, intent(in) :: strong
    integer :: i
    class(bc_t), pointer :: b
    b => null()
 
    call this%bcs_vel%apply_vector(&
         this%u%x, this%v%x, this%w%x, this%dm_Xh%size(), time, strong)
 
    call rotate_cyc(this%u%x, this%v%x, this%w%x, 1, this%c_Xh)
    call this%gs_Xh%op(this%u, gs_op_min, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
    call this%gs_Xh%op(this%v, gs_op_min, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
    call this%gs_Xh%op(this%w, gs_op_min, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
    call rotate_cyc(this%u%x, this%v%x, this%w%x, 0, this%c_Xh)
 
 
    call this%bcs_vel%apply_vector(&
         this%u%x, this%v%x, this%w%x, this%dm_Xh%size(), time, strong)
 
    call rotate_cyc(this%u%x, this%v%x, this%w%x, 1, this%c_Xh)
    call this%gs_Xh%op(this%u, gs_op_max, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
    call this%gs_Xh%op(this%v, gs_op_max, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
    call this%gs_Xh%op(this%w, gs_op_max, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
    call rotate_cyc(this%u%x, this%v%x, this%w%x, 0, this%c_Xh)
 
    do i = 1, this%bcs_vel%size()
       b => this%bcs_vel%get(i)
       b%updated = .false.
    end do
    nullify(b)
 
  end subroutine fluid_scheme_bc_apply_vel
 
  subroutine fluid_scheme_bc_apply_prs(this, time)
    class(fluid_scheme_incompressible_t), intent(inout) :: this
    type(time_state_t), intent(in) :: time
 
    integer :: i
    class(bc_t), pointer :: b
    b => null()
 
    call this%bcs_prs%apply(this%p, time)
    call this%gs_Xh%op(this%p, gs_op_min, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
 
    call this%bcs_prs%apply(this%p, time)
    call this%gs_Xh%op(this%p, gs_op_max, glb_cmd_event)
    call device_event_sync(glb_cmd_event)
 
    do i = 1, this%bcs_prs%size()
       b => this%bcs_prs%get(i)
       b%updated = .false.
    end do
    nullify(b)
 
  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)
 
  end subroutine fluid_scheme_solver_factory
 
  subroutine fluid_scheme_precon_factory(this, pc, ksp, coef, dof, gs, bclst, &
       pctype, pcparams)
    class(fluid_scheme_incompressible_t), intent(inout) :: this
    class(pc_t), allocatable, target, intent(inout) :: pc
    class(ksp_t), target, intent(inout) :: ksp
    type(coef_t), target, intent(in) :: coef
    type(dofmap_t), target, intent(in) :: dof
    type(gs_t), target, intent(inout) :: gs
    type(bc_list_t), target, intent(inout) :: bclst
    character(len=*) :: pctype
    type(json_file), intent(inout) :: pcparams
 
    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)
       call pcp%init(coef, bclst, pcparams)
    type is (phmg_t)
       call pcp%init(coef, bclst, pcparams)
    end select
 
    call ksp%set_pc(pc)
 
  end subroutine fluid_scheme_precon_factory
 
  function fluid_compute_cfl(this, dt) result(c)
    class(fluid_scheme_incompressible_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)
 
  end function fluid_compute_cfl
 
 
  subroutine fluid_scheme_update_material_properties(this, time)
    class(fluid_scheme_incompressible_t), intent(inout) :: this
    type(time_state_t), intent(in) :: time
    type(field_t), pointer :: nut
 
    call this%user_material_properties(this%name, this%material_properties, &
         time)
 
    if (len(trim(this%nut_field_name)) > 0) then
       nut => neko_registry%get_field(this%nut_field_name)
       ! Copy material property
       call field_copy(this%mu_tot, this%mu)
       ! Add turbulent contribution
       call field_addcol3(this%mu_tot, nut, this%rho)
    end if
 
    ! Since mu, rho is a field_t, and we use the %x(1,1,1,1)
    ! host array data to pass constant density and viscosity
    ! to some routines, we need to make sure that the host
    ! values are also filled
    if (neko_bcknd_device .eq. 1) then
       call device_memcpy(this%rho%x, this%rho%x_d, this%rho%size(), &
            device_to_host, sync = .false.)
    end if
  end subroutine fluid_scheme_update_material_properties
 
  subroutine fluid_scheme_set_material_properties(this, params, user)
    class(fluid_scheme_incompressible_t), target, 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_intf), pointer :: dummy_mp_ptr
    logical :: nondimensional
    real(kind=rp) :: dummy_lambda, dummy_cp
    real(kind=rp) :: const_mu, const_rho
    type(time_state_t) :: dummy_time_state
 
 
    dummy_mp_ptr => dummy_user_material_properties
 
    call neko_registry%add_field(this%dm_Xh, this%name // "_mu")
    call neko_registry%add_field(this%dm_Xh, this%name // "_mu_tot")
    call neko_registry%add_field(this%dm_Xh, this%name // "_rho")
    this%mu => neko_registry%get_field(this%name // "_mu")
    this%mu_tot => neko_registry%get_field(this%name // "_mu_tot")
    this%rho => neko_registry%get_field(this%name // "_rho")
 
    call this%material_properties%init(2)
    call this%material_properties%assign(1, this%rho)
    call this%material_properties%assign(2, this%mu)
 
    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)
       this%user_material_properties => user%material_properties
 
       call user%material_properties(this%name, this%material_properties, &
            dummy_time_state)
 
    else
       this%user_material_properties => dummy_user_material_properties
       ! 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.")
 
       else if (params%valid_path('case.fluid.Re')) then
          ! Non-dimensional case
          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_or_lookup(params, 'case.fluid.Re', const_mu)
          write(log_buf, '(A)') 'Read non-dimensional material properties'
          call neko_log%message(log_buf)
          write(log_buf, '(A,ES13.6)') 'Re         :', const_mu
          call neko_log%message(log_buf)
 
          ! Set rho to 1 since the setup is non-dimensional.
          const_rho = 1.0_rp
          ! Invert the Re to get viscosity.
          const_mu = 1.0_rp/const_mu
       else
          ! Dimensional case
          call json_get_or_lookup(params, 'case.fluid.mu', const_mu)
          call json_get_or_lookup(params, 'case.fluid.rho', const_rho)
       end if
    end if
 
    ! We need to fill the fields based on the parsed const values
    ! if the user routine is not used.
    if (associated(user%material_properties, dummy_mp_ptr)) then
       ! Fill mu and rho field with the physical value
       call field_cfill(this%mu, const_mu)
       call field_cfill(this%mu_tot, const_mu)
       call field_cfill(this%rho, const_rho)
 
 
       write(log_buf, '(A,ES13.6)') 'rho        :', const_rho
       call neko_log%message(log_buf)
       write(log_buf, '(A,ES13.6)') 'mu         :', const_mu
       call neko_log%message(log_buf)
    end if
 
    ! Copy over material property to the total one
    call field_copy(this%mu_tot, this%mu)
 
    ! Since mu, rho is a field_t, and we use the %x(1,1,1,1)
    ! host array data to pass constant density and viscosity
    ! to some routines, we need to make sure that the host
    ! values are also filled
    if (neko_bcknd_device .eq. 1) then
       call device_memcpy(this%rho%x, this%rho%x_d, this%rho%size(), &
            device_to_host, sync = .false.)
       call device_memcpy(this%mu%x, this%mu%x_d, this%mu%size(), &
            device_to_host, sync = .false.)
       call device_memcpy(this%mu_tot%x, this%mu_tot%x_d, this%mu%size(), &
            device_to_host, sync = .false.)
    end if
  end subroutine fluid_scheme_set_material_properties
 
end module fluid_scheme_incompressible