wale_cpu.f90

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module wale_cpu
  use num_types, only : rp
  use field_list, only : field_list_t
  use scratch_registry, only : neko_scratch_registry
  use registry, only : neko_registry
  use field, only : field_t
  use operators, only : dudxyz, strain_rate
  use coefs, only : coef_t
  use gs_ops, only : gs_op_add
  use math, only : col2, neko_eps
  implicit none
  private
 
  public :: wale_compute_cpu
 
contains
 
  subroutine wale_compute_cpu(if_ext, t, tstep, coef, nut, delta, c_w)
    logical, intent(in) :: if_ext
    real(kind=rp), intent(in) :: t
    integer, intent(in) :: tstep
    type(coef_t), intent(in) :: coef
    type(field_t), intent(inout) :: nut
    type(field_t), intent(in) :: delta
    real(kind=rp), intent(in) :: c_w
    type(field_t), pointer :: u, v, w
    ! the velocity gradient tensor
    type(field_t), pointer :: g11, g12, g13, g21, g22, g23, g31, g32, g33
    ! strain rate tensor
    type(field_t), pointer :: s11, s22, s33, s12, s13, s23
 
    real(kind=rp) :: gsqr_11, gsqr_12, gsqr_13, gsqr_21, gsqr_22, gsqr_23, gsqr_31, gsqr_32, gsqr_33
    real(kind=rp) :: sd11, sd22, sd33, sd12, sd13, sd23
    real(kind=rp) :: sdij_sdij
    real(kind=rp) :: sij_sij
    real(kind=rp) :: op_wale
    integer :: temp_indices(15)
    integer :: e, i
 
 
    if (if_ext .eqv. .true.) then
       u => neko_registry%get_field_by_name("u_e")
       v => neko_registry%get_field_by_name("v_e")
       w => neko_registry%get_field_by_name("w_e")
    else
       u => neko_registry%get_field_by_name("u")
       v => neko_registry%get_field_by_name("v")
       w => neko_registry%get_field_by_name("w")
    end if
 
    call neko_scratch_registry%request_field(g11, temp_indices(1), .false.)
    call neko_scratch_registry%request_field(g12, temp_indices(2), .false.)
    call neko_scratch_registry%request_field(g13, temp_indices(3), .false.)
    call neko_scratch_registry%request_field(g21, temp_indices(4), .false.)
    call neko_scratch_registry%request_field(g22, temp_indices(5), .false.)
    call neko_scratch_registry%request_field(g23, temp_indices(6), .false.)
    call neko_scratch_registry%request_field(g31, temp_indices(7), .false.)
    call neko_scratch_registry%request_field(g32, temp_indices(8), .false.)
    call neko_scratch_registry%request_field(g33, temp_indices(9), .false.)
 
    call neko_scratch_registry%request_field(s11, temp_indices(10), .false.)
    call neko_scratch_registry%request_field(s22, temp_indices(11), .false.)
    call neko_scratch_registry%request_field(s33, temp_indices(12), .false.)
    call neko_scratch_registry%request_field(s12, temp_indices(13), .false.)
    call neko_scratch_registry%request_field(s13, temp_indices(14), .false.)
    call neko_scratch_registry%request_field(s23, temp_indices(15), .false.)
 
 
    ! Compute the velocity gradient tensor g
    call dudxyz(g11%x, u%x, coef%drdx, coef%dsdx, coef%dtdx, coef)
    call dudxyz(g12%x, u%x, coef%drdy, coef%dsdy, coef%dtdy, coef)
    call dudxyz(g13%x, u%x, coef%drdz, coef%dsdz, coef%dtdz, coef)
 
    call dudxyz(g21%x, v%x, coef%drdx, coef%dsdx, coef%dtdx, coef)
    call dudxyz(g22%x, v%x, coef%drdy, coef%dsdy, coef%dtdy, coef)
    call dudxyz(g23%x, v%x, coef%drdz, coef%dsdz, coef%dtdz, coef)
 
    call dudxyz(g31%x, w%x, coef%drdx, coef%dsdx, coef%dtdx, coef)
    call dudxyz(g32%x, w%x, coef%drdy, coef%dsdy, coef%dtdy, coef)
    call dudxyz(g33%x, w%x, coef%drdz, coef%dsdz, coef%dtdz, coef)
 
    call coef%gs_h%op(g11, gs_op_add)
    call coef%gs_h%op(g12, gs_op_add)
    call coef%gs_h%op(g13, gs_op_add)
    call coef%gs_h%op(g21, gs_op_add)
    call coef%gs_h%op(g22, gs_op_add)
    call coef%gs_h%op(g23, gs_op_add)
    call coef%gs_h%op(g31, gs_op_add)
    call coef%gs_h%op(g32, gs_op_add)
    call coef%gs_h%op(g33, gs_op_add)
 
    ! Compute components of the strain rate tensor
    call strain_rate(s11%x, s22%x, s33%x, s12%x, s13%x, s23%x, &
         u%x, v%x, w%x, coef)
 
    call coef%gs_h%op(s11, gs_op_add)
    call coef%gs_h%op(s22, gs_op_add)
    call coef%gs_h%op(s33, gs_op_add)
    call coef%gs_h%op(s12, gs_op_add)
    call coef%gs_h%op(s13, gs_op_add)
    call coef%gs_h%op(s23, gs_op_add)
 
 
    do concurrent(e = 1:coef%msh%nelv)
       do concurrent(i = 1:coef%Xh%lxyz)
          ! gij^2 = g_ik * g_kj
          gsqr_11 = g11%x(i,1,1,e)*g11%x(i,1,1,e) + &
               g12%x(i,1,1,e)*g21%x(i,1,1,e) + &
               g13%x(i,1,1,e)*g31%x(i,1,1,e)
          gsqr_12 = g11%x(i,1,1,e)*g12%x(i,1,1,e) + &
               g12%x(i,1,1,e)*g22%x(i,1,1,e) + &
               g13%x(i,1,1,e)*g32%x(i,1,1,e)
          gsqr_13 = g11%x(i,1,1,e)*g13%x(i,1,1,e) + &
               g12%x(i,1,1,e)*g23%x(i,1,1,e) + &
               g13%x(i,1,1,e)*g33%x(i,1,1,e)
          gsqr_21 = g21%x(i,1,1,e)*g11%x(i,1,1,e) + &
               g22%x(i,1,1,e)*g21%x(i,1,1,e) + &
               g23%x(i,1,1,e)*g31%x(i,1,1,e)
          gsqr_22 = g21%x(i,1,1,e)*g12%x(i,1,1,e) + &
               g22%x(i,1,1,e)*g22%x(i,1,1,e) + &
               g23%x(i,1,1,e)*g32%x(i,1,1,e)
          gsqr_23 = g21%x(i,1,1,e)*g13%x(i,1,1,e) + &
               g22%x(i,1,1,e)*g23%x(i,1,1,e) + &
               g23%x(i,1,1,e)*g33%x(i,1,1,e)
          gsqr_31 = g31%x(i,1,1,e)*g11%x(i,1,1,e) + &
               g32%x(i,1,1,e)*g21%x(i,1,1,e) + &
               g33%x(i,1,1,e)*g31%x(i,1,1,e)
          gsqr_32 = g31%x(i,1,1,e)*g12%x(i,1,1,e) + &
               g32%x(i,1,1,e)*g22%x(i,1,1,e) + &
               g33%x(i,1,1,e)*g32%x(i,1,1,e)
          gsqr_33 = g31%x(i,1,1,e)*g13%x(i,1,1,e) + &
               g32%x(i,1,1,e)*g23%x(i,1,1,e) + &
               g33%x(i,1,1,e)*g33%x(i,1,1,e)
 
          ! sdij components
          sd11 = gsqr_11 - ( (gsqr_11 + gsqr_22 + gsqr_33) / 3.0_rp)
          sd22 = gsqr_22 - ( (gsqr_11 + gsqr_22 + gsqr_33) / 3.0_rp)
          sd33 = gsqr_33 - ( (gsqr_11 + gsqr_22 + gsqr_33) / 3.0_rp)
          sd12 = 0.5_rp * (gsqr_12 + gsqr_21)
          sd13 = 0.5_rp * (gsqr_13 + gsqr_31)
          sd23 = 0.5_rp * (gsqr_23 + gsqr_32)
 
          ! Sdij*Sdij
          sdij_sdij = sd11*sd11 + sd22*sd22 + sd33*sd33 + &
               2.0_rp * (sd12*sd12 + sd13*sd13 + sd23*sd23)
          ! Sij*Sij
          sij_sij = s11%x(i,1,1,e)*s11%x(i,1,1,e) + s22%x(i,1,1,e)*s22%x(i,1,1,e) + &
               s33%x(i,1,1,e)*s33%x(i,1,1,e) + 2.0_rp * (s12%x(i,1,1,e)*s12%x(i,1,1,e) + &
               s13%x(i,1,1,e)*s13%x(i,1,1,e) + s23%x(i,1,1,e)*s23%x(i,1,1,e))
 
          ! Wale operator
          op_wale = sdij_sdij**(3.0_rp / 2.0_rp) / &
               max((sij_sij**(5.0_rp / 2.0_rp) + sdij_sdij**(5.0_rp / 4.0_rp)), neko_eps)
 
          ! turbulent viscosity
          nut%x(i,1,1,e) = c_w**2 * delta%x(i,1,1,e)**2 * op_wale * coef%mult(i,1,1,e)
       end do
    end do
 
    call neko_scratch_registry%relinquish_field(temp_indices)
  end subroutine wale_compute_cpu
 
end module wale_cpu