vreman_cpu.f90

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module vreman_cpu
  use num_types, only : rp
  use field_list, only : field_list_t
  use math, only : cadd, neko_eps
  use scratch_registry, only : neko_scratch_registry
  use field_registry, only : neko_field_registry
  use field, only : field_t
  use operators, only : dudxyz
  use coefs, only : coef_t
  use gs_ops, only : gs_op_add
   implicit none
  private
 
  public :: vreman_compute_cpu
 
contains
 
  subroutine vreman_compute_cpu(t, tstep, coef, nut, delta, c)
    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
    ! This is the alpha tensor in the paper
    type(field_t), pointer :: a11, a12, a13, a21, a22, a23, a31, a32, a33
    type(field_t), pointer :: u, v, w
 
    real(kind=rp) :: beta11
    real(kind=rp) :: beta12
    real(kind=rp) :: beta13
    real(kind=rp) :: beta22
    real(kind=rp) :: beta23
    real(kind=rp) :: beta33
    real(kind=rp) :: b_beta
    real(kind=rp) :: aijaij
    integer :: temp_indices(9)
    integer :: e, i
 
    u => neko_field_registry%get_field_by_name("u")
    v => neko_field_registry%get_field_by_name("v")
    w => neko_field_registry%get_field_by_name("w")
 
    call neko_scratch_registry%request_field(a11, temp_indices(1))
    call neko_scratch_registry%request_field(a12, temp_indices(2))
    call neko_scratch_registry%request_field(a13, temp_indices(3))
    call neko_scratch_registry%request_field(a21, temp_indices(4))
    call neko_scratch_registry%request_field(a22, temp_indices(5))
    call neko_scratch_registry%request_field(a23, temp_indices(6))
    call neko_scratch_registry%request_field(a31, temp_indices(7))
    call neko_scratch_registry%request_field(a32, temp_indices(8))
    call neko_scratch_registry%request_field(a33, temp_indices(9))
 
 
    ! Compute the derivatives of the velocity (the alpha tensor)
    call dudxyz (a11%x, u%x, coef%drdx, coef%dsdx, coef%dtdx, coef)
    call dudxyz (a12%x, u%x, coef%drdy, coef%dsdy, coef%dtdy, coef)
    call dudxyz (a13%x, u%x, coef%drdz, coef%dsdz, coef%dtdz, coef)
 
    call dudxyz (a21%x, v%x, coef%drdx, coef%dsdx, coef%dtdx, coef)
    call dudxyz (a22%x, v%x, coef%drdy, coef%dsdy, coef%dtdy, coef)
    call dudxyz (a23%x, v%x, coef%drdz, coef%dsdz, coef%dtdz, coef)
 
    call dudxyz (a31%x, w%x, coef%drdx, coef%dsdx, coef%dtdx, coef)
    call dudxyz (a32%x, w%x, coef%drdy, coef%dsdy, coef%dtdy, coef)
    call dudxyz (a33%x, w%x, coef%drdz, coef%dsdz, coef%dtdz, coef)
 
    call coef%gs_h%op(a11%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a12%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a13%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a21%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a22%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a23%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a31%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a32%x, a11%dof%size(), gs_op_add)
    call coef%gs_h%op(a33%x, a11%dof%size(), gs_op_add)
 
    do concurrent(i = 1:a11%dof%size())
       a11%x(i,1,1,1) = a11%x(i,1,1,1) * coef%mult(i,1,1,1)
       a12%x(i,1,1,1) = a12%x(i,1,1,1) * coef%mult(i,1,1,1)
       a13%x(i,1,1,1) = a13%x(i,1,1,1) * coef%mult(i,1,1,1)
       a21%x(i,1,1,1) = a21%x(i,1,1,1) * coef%mult(i,1,1,1)
       a22%x(i,1,1,1) = a22%x(i,1,1,1) * coef%mult(i,1,1,1)
       a23%x(i,1,1,1) = a23%x(i,1,1,1) * coef%mult(i,1,1,1)
       a31%x(i,1,1,1) = a31%x(i,1,1,1) * coef%mult(i,1,1,1)
       a32%x(i,1,1,1) = a32%x(i,1,1,1) * coef%mult(i,1,1,1)
       a33%x(i,1,1,1) = a33%x(i,1,1,1) * coef%mult(i,1,1,1)
    end do
 
    do concurrent(e = 1:coef%msh%nelv)
       do concurrent(i = 1:coef%Xh%lxyz)
          ! beta_ij = alpha_mi alpha_mj
          beta11 = a11%x(i,1,1,e)**2 + a21%x(i,1,1,e)**2 + a31%x(i,1,1,e)**2
          beta22 = a12%x(i,1,1,e)**2 + a22%x(i,1,1,e)**2 + a32%x(i,1,1,e)**2
          beta33 = a13%x(i,1,1,e)**2 + a23%x(i,1,1,e)**2 + a33%x(i,1,1,e)**2
          beta12 = a11%x(i,1,1,e)*a12%x(i,1,1,e) + &
                   a21%x(i,1,1,e)*a22%x(i,1,1,e) + &
                   a31%x(i,1,1,e)*a32%x(i,1,1,e)
          beta13 = a11%x(i,1,1,e)*a13%x(i,1,1,e) + &
                   a21%x(i,1,1,e)*a23%x(i,1,1,e) + &
                   a31%x(i,1,1,e)*a33%x(i,1,1,e)
          beta23 = a12%x(i,1,1,e)*a13%x(i,1,1,e) + &
                   a22%x(i,1,1,e)*a23%x(i,1,1,e) + &
                   a32%x(i,1,1,e)*a33%x(i,1,1,e)
 
          b_beta = beta11*beta22 - beta12*beta12 + beta11*beta33 - beta13*beta13 &
                  + beta22*beta33 - beta23*beta23
 
          b_beta = max(0.0_rp, b_beta)
 
          ! alpha_ij alpha_ij
          aijaij = beta11 + beta22 + beta33
 
          nut%x(i,1,1,e) = c*delta%x(i,1,1,e)*delta%x(i,1,1,e) &
                            * sqrt(b_beta/(aijaij + neko_eps))
       end do
    end do
 
    call neko_scratch_registry%relinquish_field(temp_indices)
  end subroutine vreman_compute_cpu
 
end module vreman_cpu