euler_res_cpu.f90

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!? It handles the time advancement of primitive variables using Runge-Kutta methods
!? and evaluates the right-hand side terms of the Euler equations including artificial viscosity.
module euler_res_cpu
  use euler_residual, only : euler_rhs_t
  use field, only : field_t
  use ax_product, only : ax_t
  use coefs, only : coef_t
  use gather_scatter, only : gs_t
  use num_types, only : rp
  use operators, only: div, rotate_cyc
  use gs_ops, only : gs_op_add
  use scratch_registry, only: neko_scratch_registry
  use runge_kutta_time_scheme, only : runge_kutta_time_scheme_t
  use field_list, only : field_list_t
  implicit none
  private
 
  type, public, extends(euler_rhs_t) :: euler_res_cpu_t
   contains
     procedure, nopass :: step => advance_primitive_variables_cpu
     procedure, nopass :: evaluate_rhs_cpu
  end type euler_res_cpu_t
 
contains
  subroutine advance_primitive_variables_cpu(rho_field, m_x, m_y, m_z, &
       E, p, u, v, w, Ax, &
       coef, gs, h, effective_visc, rk_scheme, dt)
    type(field_t), intent(inout) :: rho_field, m_x, m_y, m_z, E
    type(field_t), intent(in) :: p, u, v, w, h, effective_visc
    class(ax_t), intent(inout) :: Ax
    type(coef_t), intent(inout) :: coef
    type(gs_t), intent(inout) :: gs
    class(runge_kutta_time_scheme_t), intent(in) :: rk_scheme
    real(kind=rp), intent(in) :: dt
    integer :: n, s, i, j, k
    type(field_t), pointer :: k_rho_1, k_rho_2, k_rho_3, k_rho_4, &
         k_m_x_1, k_m_x_2, k_m_x_3, k_m_x_4, &
         k_m_y_1, k_m_y_2, k_m_y_3, k_m_y_4, &
         k_m_z_1, k_m_z_2, k_m_z_3, k_m_z_4, &
         k_E_1, k_E_2, k_E_3, k_E_4, &
         temp_rho, temp_m_x, temp_m_y, temp_m_z, temp_E
    integer :: tmp_indices(25)
    type(field_list_t) :: k_rho, k_m_x, k_m_y, k_m_z, k_E
 
    n = p%dof%size()
    s = rk_scheme%order
    call neko_scratch_registry%request_field(k_rho_1, tmp_indices(1), .true.)
    call neko_scratch_registry%request_field(k_rho_2, tmp_indices(2), .true.)
    call neko_scratch_registry%request_field(k_rho_3, tmp_indices(3), .true.)
    call neko_scratch_registry%request_field(k_rho_4, tmp_indices(4), .true.)
    call neko_scratch_registry%request_field(k_m_x_1, tmp_indices(5), .true.)
    call neko_scratch_registry%request_field(k_m_x_2, tmp_indices(6), .true.)
    call neko_scratch_registry%request_field(k_m_x_3, tmp_indices(7), .true.)
    call neko_scratch_registry%request_field(k_m_x_4, tmp_indices(8), .true.)
    call neko_scratch_registry%request_field(k_m_y_1, tmp_indices(9), .true.)
    call neko_scratch_registry%request_field(k_m_y_2, tmp_indices(10), .true.)
    call neko_scratch_registry%request_field(k_m_y_3, tmp_indices(11), .true.)
    call neko_scratch_registry%request_field(k_m_y_4, tmp_indices(12), .true.)
    call neko_scratch_registry%request_field(k_m_z_1, tmp_indices(13), .true.)
    call neko_scratch_registry%request_field(k_m_z_2, tmp_indices(14), .true.)
    call neko_scratch_registry%request_field(k_m_z_3, tmp_indices(15), .true.)
    call neko_scratch_registry%request_field(k_m_z_4, tmp_indices(16), .true.)
    call neko_scratch_registry%request_field(k_e_1, tmp_indices(17), .true.)
    call neko_scratch_registry%request_field(k_e_2, tmp_indices(18), .true.)
    call neko_scratch_registry%request_field(k_e_3, tmp_indices(19), .true.)
    call neko_scratch_registry%request_field(k_e_4, tmp_indices(20), .true.)
    call neko_scratch_registry%request_field(temp_rho, tmp_indices(21), .false.)
    call neko_scratch_registry%request_field(temp_m_x, tmp_indices(22), .false.)
    call neko_scratch_registry%request_field(temp_m_y, tmp_indices(23), .false.)
    call neko_scratch_registry%request_field(temp_m_z, tmp_indices(24), .false.)
    call neko_scratch_registry%request_field(temp_e, tmp_indices(25), .false.)
 
    ! Initialize Runge-Kutta stage variables for each conserved quantity
    call k_rho%init(4)
    call k_rho%assign(1, k_rho_1)
    call k_rho%assign(2, k_rho_2)
    call k_rho%assign(3, k_rho_3)
    call k_rho%assign(4, k_rho_4)
    call k_m_x%init(4)
    call k_m_x%assign(1, k_m_x_1)
    call k_m_x%assign(2, k_m_x_2)
    call k_m_x%assign(3, k_m_x_3)
    call k_m_x%assign(4, k_m_x_4)
    call k_m_y%init(4)
    call k_m_y%assign(1, k_m_y_1)
    call k_m_y%assign(2, k_m_y_2)
    call k_m_y%assign(3, k_m_y_3)
    call k_m_y%assign(4, k_m_y_4)
    call k_m_z%init(4)
    call k_m_z%assign(1, k_m_z_1)
    call k_m_z%assign(2, k_m_z_2)
    call k_m_z%assign(3, k_m_z_3)
    call k_m_z%assign(4, k_m_z_4)
    call k_e%init(4)
    call k_e%assign(1, k_e_1)
    call k_e%assign(2, k_e_2)
    call k_e%assign(3, k_e_3)
    call k_e%assign(4, k_e_4)
 
    ! Loop over Runge-Kutta stages
    do i = 1, s
       ! Copy current solution state to temporary arrays for this RK stage
       do concurrent(k = 1:n)
          temp_rho%x(k,1,1,1) = rho_field%x(k,1,1,1)
          temp_m_x%x(k,1,1,1) = m_x%x(k,1,1,1)
          temp_m_y%x(k,1,1,1) = m_y%x(k,1,1,1)
          temp_m_z%x(k,1,1,1) = m_z%x(k,1,1,1)
          temp_e%x(k,1,1,1) = e%x(k,1,1,1)
       end do
 
       ! Accumulate previous stage contributions using RK coefficients
       do j = 1, i-1
          do concurrent(k = 1:n)
             temp_rho%x(k,1,1,1) = temp_rho%x(k,1,1,1) &
                  + dt * rk_scheme%coeffs_A(i, j) * k_rho%items(j)%ptr%x(k,1,1,1)
             temp_m_x%x(k,1,1,1) = temp_m_x%x(k,1,1,1) &
                  + dt * rk_scheme%coeffs_A(i, j) * k_m_x%items(j)%ptr%x(k,1,1,1)
             temp_m_y%x(k,1,1,1) = temp_m_y%x(k,1,1,1) &
                  + dt * rk_scheme%coeffs_A(i, j) * k_m_y%items(j)%ptr%x(k,1,1,1)
             temp_m_z%x(k,1,1,1) = temp_m_z%x(k,1,1,1) &
                  + dt * rk_scheme%coeffs_A(i, j) * k_m_z%items(j)%ptr%x(k,1,1,1)
             temp_e%x(k,1,1,1) = temp_e%x(k,1,1,1) &
                  + dt * rk_scheme%coeffs_A(i, j) * k_e%items(j)%ptr%x(k,1,1,1)
          end do
       end do
 
       ! Evaluate RHS terms for current stage using intermediate solution values
       call evaluate_rhs_cpu(k_rho%items(i)%ptr, k_m_x%items(i)%ptr, &
            k_m_y%items(i)%ptr, k_m_z%items(i)%ptr, &
            k_e%items(i)%ptr, &
            temp_rho, temp_m_x, temp_m_y, temp_m_z, temp_e, &
            p, u, v, w, ax, &
            coef, gs, h, effective_visc)
    end do
 
    ! Update the solution
    do i = 1, s
       do concurrent(k = 1:n)
          rho_field%x(k,1,1,1) = rho_field%x(k,1,1,1) &
               + dt * rk_scheme%coeffs_b(i) * k_rho%items(i)%ptr%x(k,1,1,1)
          m_x%x(k,1,1,1) = m_x%x(k,1,1,1) &
               + dt * rk_scheme%coeffs_b(i) * k_m_x%items(i)%ptr%x(k,1,1,1)
          m_y%x(k,1,1,1) = m_y%x(k,1,1,1) &
               + dt * rk_scheme%coeffs_b(i) * k_m_y%items(i)%ptr%x(k,1,1,1)
          m_z%x(k,1,1,1) = m_z%x(k,1,1,1) &
               + dt * rk_scheme%coeffs_b(i) * k_m_z%items(i)%ptr%x(k,1,1,1)
          e%x(k,1,1,1) = e%x(k,1,1,1) &
               + dt * rk_scheme%coeffs_b(i) * k_e%items(i)%ptr%x(k,1,1,1)
       end do
    end do
 
    call neko_scratch_registry%relinquish_field(tmp_indices)
 
  end subroutine advance_primitive_variables_cpu
 
  subroutine evaluate_rhs_cpu(rhs_rho_field, rhs_m_x, rhs_m_y, rhs_m_z, rhs_E, &
       rho_field, m_x, m_y, m_z, E, p, u, v, w, Ax, &
       coef, gs, h, effective_visc)
    type(field_t), intent(inout) :: rhs_rho_field, &
         rhs_m_x, rhs_m_y, rhs_m_z, rhs_E
    type(field_t), intent(inout) :: rho_field, m_x, m_y, m_z, E
    type(field_t), intent(in) :: p, u, v, w, h, effective_visc
    class(ax_t), intent(inout) :: Ax
    type(coef_t), intent(inout) :: coef
    type(gs_t), intent(inout) :: gs
    integer :: i, n
    type(field_t), pointer :: f_x, f_y, f_z, &
         visc_rho, visc_m_x, visc_m_y, visc_m_z, visc_E
    integer :: tmp_indices(8)
 
    n = coef%dof%size()
    call neko_scratch_registry%request_field(f_x, tmp_indices(1), .false.)
    call neko_scratch_registry%request_field(f_y, tmp_indices(2), .false.)
    call neko_scratch_registry%request_field(f_z, tmp_indices(3), .false.)
 
    ! Compute density flux divergence
    call div(rhs_rho_field%x, m_x%x, m_y%x, m_z%x, coef)
 
    ! Compute momentum flux divergences
    ! m_x
    do concurrent(i = 1:n)
       f_x%x(i,1,1,1) = m_x%x(i,1,1,1) * m_x%x(i,1,1,1) / rho_field%x(i, 1, 1, 1) &
            + p%x(i,1,1,1)
       f_y%x(i,1,1,1) = m_x%x(i,1,1,1) * m_y%x(i,1,1,1) / rho_field%x(i, 1, 1, 1)
       f_z%x(i,1,1,1) = m_x%x(i,1,1,1) * m_z%x(i,1,1,1) / rho_field%x(i, 1, 1, 1)
    end do
    call div(rhs_m_x%x, f_x%x, f_y%x, f_z%x, coef)
    ! m_y
    do concurrent(i = 1:n)
       f_x%x(i,1,1,1) = m_y%x(i,1,1,1) * m_x%x(i,1,1,1) / rho_field%x(i, 1, 1, 1)
       f_y%x(i,1,1,1) = m_y%x(i,1,1,1) * m_y%x(i,1,1,1) / rho_field%x(i, 1, 1, 1) &
            + p%x(i,1,1,1)
       f_z%x(i,1,1,1) = m_y%x(i,1,1,1) * m_z%x(i,1,1,1) / rho_field%x(i, 1, 1, 1)
    end do
    call div(rhs_m_y%x, f_x%x, f_y%x, f_z%x, coef)
    ! m_z
    do concurrent(i = 1:n)
       f_x%x(i,1,1,1) = m_z%x(i,1,1,1) * m_x%x(i,1,1,1) / rho_field%x(i, 1, 1, 1)
       f_y%x(i,1,1,1) = m_z%x(i,1,1,1) * m_y%x(i,1,1,1) / rho_field%x(i, 1, 1, 1)
       f_z%x(i,1,1,1) = m_z%x(i,1,1,1) * m_z%x(i,1,1,1) / rho_field%x(i, 1, 1, 1) &
            + p%x(i,1,1,1)
    end do
    call div(rhs_m_z%x, f_x%x, f_y%x, f_z%x, coef)
 
    ! Compute energy flux divergence
    do concurrent(i = 1:n)
       f_x%x(i,1,1,1) = (e%x(i,1,1,1) + p%x(i,1,1,1)) * u%x(i,1,1,1)
       f_y%x(i,1,1,1) = (e%x(i,1,1,1) + p%x(i,1,1,1)) * v%x(i,1,1,1)
       f_z%x(i,1,1,1) = (e%x(i,1,1,1) + p%x(i,1,1,1)) * w%x(i,1,1,1)
    end do
    call div(rhs_e%x, f_x%x, f_y%x, f_z%x, coef)
 
    ! gs
    call gs%op(rhs_rho_field, gs_op_add)
    call rotate_cyc(rhs_m_x%x, rhs_m_y%x, rhs_m_z%x, 1, coef)
    call gs%op(rhs_m_x, gs_op_add)
    call gs%op(rhs_m_y, gs_op_add)
    call gs%op(rhs_m_z, gs_op_add)
    call rotate_cyc(rhs_m_x%x, rhs_m_y%x, rhs_m_z%x, 0, coef)
    call gs%op(rhs_e, gs_op_add)
    do concurrent(i = 1:rhs_e%dof%size())
       rhs_rho_field%x(i,1,1,1) = rhs_rho_field%x(i,1,1,1) * coef%mult(i,1,1,1)
       rhs_m_x%x(i,1,1,1) = rhs_m_x%x(i,1,1,1) * coef%mult(i,1,1,1)
       rhs_m_y%x(i,1,1,1) = rhs_m_y%x(i,1,1,1) * coef%mult(i,1,1,1)
       rhs_m_z%x(i,1,1,1) = rhs_m_z%x(i,1,1,1) * coef%mult(i,1,1,1)
       rhs_e%x(i,1,1,1) = rhs_e%x(i,1,1,1) * coef%mult(i,1,1,1)
    end do
 
    call neko_scratch_registry%request_field(visc_rho, tmp_indices(4), .false.)
    call neko_scratch_registry%request_field(visc_m_x, tmp_indices(5), .false.)
    call neko_scratch_registry%request_field(visc_m_y, tmp_indices(6), .false.)
    call neko_scratch_registry%request_field(visc_m_z, tmp_indices(7), .false.)
    call neko_scratch_registry%request_field(visc_e, tmp_indices(8), .false.)
 
    ! Set h1 coefficient to the effective viscosity for the Laplacian operator
    do concurrent(i = 1:n)
       coef%h1(i,1,1,1) = effective_visc%x(i,1,1,1)
    end do
 
    ! Calculate artificial diffusion with variable viscosity
    call ax%compute(visc_rho%x, rho_field%x, coef, p%msh, p%Xh)
    call ax%compute(visc_m_x%x, m_x%x, coef, p%msh, p%Xh)
    call ax%compute(visc_m_y%x, m_y%x, coef, p%msh, p%Xh)
    call ax%compute(visc_m_z%x, m_z%x, coef, p%msh, p%Xh)
    call ax%compute(visc_e%x, e%x, coef, p%msh, p%Xh)
 
    ! Reset h1 coefficient back to 1.0 for other operations
    do concurrent(i = 1:n)
       coef%h1(i,1,1,1) = 1.0_rp
    end do
 
    ! gs
    call gs%op(visc_rho, gs_op_add)
    call rotate_cyc(visc_m_x%x, visc_m_y%x, visc_m_z%x, 1, coef)
    call gs%op(visc_m_x, gs_op_add)
    call gs%op(visc_m_y, gs_op_add)
    call gs%op(visc_m_z, gs_op_add)
    call rotate_cyc(visc_m_x%x, visc_m_y%x, visc_m_z%x, 0, coef)
    call gs%op(visc_e, gs_op_add)
 
    ! Move div to the rhs and apply artificial viscosity
    ! The viscosity coefficient is already included in the Laplacian operator
    do concurrent(i = 1:n)
       rhs_rho_field%x(i,1,1,1) = -rhs_rho_field%x(i,1,1,1) &
            - coef%Binv(i,1,1,1) * visc_rho%x(i,1,1,1)
       rhs_m_x%x(i,1,1,1) = -rhs_m_x%x(i,1,1,1) &
            - coef%Binv(i,1,1,1) * visc_m_x%x(i,1,1,1)
       rhs_m_y%x(i,1,1,1) = -rhs_m_y%x(i,1,1,1) &
            - coef%Binv(i,1,1,1) * visc_m_y%x(i,1,1,1)
       rhs_m_z%x(i,1,1,1) = -rhs_m_z%x(i,1,1,1) &
            - coef%Binv(i,1,1,1) * visc_m_z%x(i,1,1,1)
       rhs_e%x(i,1,1,1) = -rhs_e%x(i,1,1,1) &
            - coef%Binv(i,1,1,1) * visc_e%x(i,1,1,1)
    end do
 
    call neko_scratch_registry%relinquish_field(tmp_indices)
  end subroutine evaluate_rhs_cpu
 
end module euler_res_cpu