write_energy_diagnostics_row Subroutine

   subroutine write_energy_diagnostics_row(mesh, flow, params, energy, step, time)
      type(mesh_t), intent(in) :: mesh
      type(flow_mpi_t), intent(in) :: flow
      type(case_params_t), intent(in) :: params
      type(energy_fields_t), intent(in) :: energy
      integer, intent(in) :: step
      real(rk), intent(in) :: time

      integer :: c, unit_id, ierr
      character(len=256 + 32) :: filename
      real(rk) :: vol, old_T
      real(rk) :: local_min_T, local_max_T, local_sum_T
      real(rk) :: local_min_h, local_max_h, local_sum_h
      real(rk) :: local_min_qrad, local_max_qrad, local_integral_qrad
      real(rk) :: local_volume
      real(rk) :: local_max_delta_T, local_delta_h2, local_h_old2
      real(rk) :: global_min_T, global_max_T, global_sum_T
      real(rk) :: global_min_h, global_max_h, global_sum_h
      real(rk) :: global_min_qrad, global_max_qrad, global_integral_qrad
      real(rk) :: global_volume
      real(rk) :: global_max_delta_T, global_delta_h2, global_h_old2
      real(rk) :: mean_T, mean_h, rel_h_residual
      logical, save :: printed_thermo_mode = .false.
      if (.not. params%write_diagnostics) return
      if (.not. params%enable_energy) return

      if (.not. allocated(energy%T) .or. .not. allocated(energy%h) .or. &
          .not. allocated(energy%h_old) .or. .not. allocated(energy%qrad)) then
         call fatal_error('energy', 'energy diagnostics requested but energy arrays are not allocated')
      end if

      local_min_T = huge(0.0_rk)
      local_max_T = -huge(0.0_rk)
      local_sum_T = zero
      local_min_h = huge(0.0_rk)
      local_max_h = -huge(0.0_rk)
      local_sum_h = zero
      local_min_qrad = huge(0.0_rk)
      local_max_qrad = -huge(0.0_rk)
      local_integral_qrad = zero
      local_volume = zero
      local_max_delta_T = zero
      local_delta_h2 = zero
      local_h_old2 = zero

      do c = 1, mesh%ncells
         if (.not. flow%owned(c)) cycle

         vol = mesh%cells(c)%volume
         local_volume = local_volume + vol

         local_min_T = min(local_min_T, energy%T(c))
         local_max_T = max(local_max_T, energy%T(c))
         local_sum_T = local_sum_T + energy%T(c) * vol

         local_min_h = min(local_min_h, energy%h(c))
         local_max_h = max(local_max_h, energy%h(c))
         local_sum_h = local_sum_h + energy%h(c) * vol

         local_min_qrad = min(local_min_qrad, energy%qrad(c))
         local_max_qrad = max(local_max_qrad, energy%qrad(c))
         local_integral_qrad = local_integral_qrad + energy%qrad(c) * vol

         if (allocated(energy%T_old)) then
            old_T = energy%T_old(c)
         else
            old_T = params%energy_reference_T + &
                    (energy%h_old(c) - params%energy_reference_h) / params%energy_cp
         end if
         local_max_delta_T = max(local_max_delta_T, abs(energy%T(c) - old_T))
         local_delta_h2 = local_delta_h2 + (energy%h(c) - energy%h_old(c))**2 * vol
         local_h_old2 = local_h_old2 + energy%h_old(c)**2 * vol
      end do

      call MPI_Allreduce(local_min_T, global_min_T, 1, MPI_DOUBLE_PRECISION, MPI_MIN, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing min_T')
      call MPI_Allreduce(local_max_T, global_max_T, 1, MPI_DOUBLE_PRECISION, MPI_MAX, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing max_T')
      call MPI_Allreduce(local_sum_T, global_sum_T, 1, MPI_DOUBLE_PRECISION, MPI_SUM, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing sum_T')

      call MPI_Allreduce(local_min_h, global_min_h, 1, MPI_DOUBLE_PRECISION, MPI_MIN, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing min_h')
      call MPI_Allreduce(local_max_h, global_max_h, 1, MPI_DOUBLE_PRECISION, MPI_MAX, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing max_h')
      call MPI_Allreduce(local_sum_h, global_sum_h, 1, MPI_DOUBLE_PRECISION, MPI_SUM, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing sum_h')

      call MPI_Allreduce(local_min_qrad, global_min_qrad, 1, MPI_DOUBLE_PRECISION, MPI_MIN, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing min_qrad')
      call MPI_Allreduce(local_max_qrad, global_max_qrad, 1, MPI_DOUBLE_PRECISION, MPI_MAX, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing max_qrad')
      call MPI_Allreduce(local_integral_qrad, global_integral_qrad, 1, MPI_DOUBLE_PRECISION, MPI_SUM, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing integral_qrad')

      call MPI_Allreduce(local_volume, global_volume, 1, MPI_DOUBLE_PRECISION, MPI_SUM, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing energy volume')
      call MPI_Allreduce(local_max_delta_T, global_max_delta_T, 1, MPI_DOUBLE_PRECISION, MPI_MAX, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing max_delta_T')
      call MPI_Allreduce(local_delta_h2, global_delta_h2, 1, MPI_DOUBLE_PRECISION, MPI_SUM, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing delta_h2')
      call MPI_Allreduce(local_h_old2, global_h_old2, 1, MPI_DOUBLE_PRECISION, MPI_SUM, flow%comm, ierr)
      if (ierr /= MPI_SUCCESS) call fatal_error('energy', 'MPI failure reducing h_old2')

      if (global_volume > tiny_safe) then
         mean_T = global_sum_T / global_volume
         mean_h = global_sum_h / global_volume
      else
         mean_T = zero
         mean_h = zero
      end if

      rel_h_residual = sqrt(global_delta_h2) / max(sqrt(global_h_old2), tiny_safe)

      if (flow%rank /= 0) return

      filename = trim(params%output_dir)//'/energy_diagnostics.csv'
      open(newunit=unit_id, file=trim(filename), status='old', position='append', action='write')

      write(unit_id,'(i0,12(",",es16.8))') step, time, global_min_T, global_max_T, mean_T, &
         global_min_h, global_max_h, mean_h, global_min_qrad, global_max_qrad, &
         global_integral_qrad, global_max_delta_T, rel_h_residual

      close(unit_id)
      if (params%enable_cantera_thermo .and. step > 0 .and. .not. printed_thermo_mode) then
         if (params%enable_species) then
            write(output_unit,'(a,i0)') 'Cantera thermo mode: transported species composition, nspecies = ', params%nspecies
         else
            write(output_unit,'(a,a)') 'Cantera thermo mode: default single species = ', trim(params%thermo_default_species)
         end if
         printed_thermo_mode = .true.
      end if

      write(output_unit,'(a,i0,2x,a,es12.5,2x,a,es12.5,2x,a,es12.5,2x,a,es12.5,2x,a,es12.5)') &
         'energy step=', step, 'Tmin=', global_min_T, 'Tmax=', global_max_T, &
         'Tmean=', mean_T, 'dTmax=', global_max_delta_T, 'rel_h=', rel_h_residual
   end subroutine write_energy_diagnostics_row