dEuler_dt Function

private function dEuler_dt(self, t) result(dState_dt)

Time derivative of Euler field, the residuals function.

Arguments

Type	Intent	Optional	Attributes		Name
class(euler_1D),	intent(in)			::	self	Euler field.
real(kind=R_P),	intent(in),	optional		::	t	Time.

Return Value class(integrand), allocatable

Euler field time derivative.

Calls

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Source Code

dEuler_dt

Source Code

  function dEuler_dt(self, t) result(dState_dt)
  !---------------------------------------------------------------------------------------------------------------------------------
  !< Time derivative of Euler field, the residuals function.
  !---------------------------------------------------------------------------------------------------------------------------------
  class(euler_1D),        intent(IN) :: self      !< Euler field.
  real(R_P),    optional, intent(IN) :: t         !< Time.
  class(integrand), allocatable      :: dState_dt !< Euler field time derivative.
  real(R_P), allocatable             :: F(:,:)    !< Fluxes of conservative variables.
  real(R_P), allocatable             :: P(:,:)    !< Primitive variables.
  real(R_P), allocatable             :: PR(:,:,:) !< Left (1) and right (2) (reconstructed) interface values of primitive variables.
  integer(I_P)                       :: i         !< Counter.
  !---------------------------------------------------------------------------------------------------------------------------------

  !---------------------------------------------------------------------------------------------------------------------------------
  associate (Ni=>self%Ni, Ng=>self%Ng, Nc=>self%Nc, Np=>self%Np, Ns=>self%Ns, U=>self%U, previous=>self%previous)
    ! allocate temporary arrays
    allocate(F(1:Nc, 0:Ni)) ; F = 0._R_P
    allocate(P(1:Np, 1-Ng:Ni+Ng)) ; P = 0._R_P
    allocate(PR(1:Np, 1:2, 0:Ni+1)) ; PR = 0._R_P
    ! compute primitive variables
    do i=1, Ni
      P(:, i) = self%conservative2primitive(U(:, i))
    enddo
    call self%impose_boundary_conditions(primitive=P)
    call self%reconstruct_interfaces_states(primitive=P, r_primitive=PR)
    ! compute fluxes by solving Rimeann Problems at each interface
    do i=0, Ni
      call self%riemann_solver(r1=PR(Ns+3, 2, i  ), u1=PR(Ns+1, 2, i  ), p1=PR(Ns+2, 2, i  ), g1=PR(Ns+4, 2, i  ), &
                               r4=PR(Ns+3, 1, i+1), u4=PR(Ns+1, 1, i+1), p4=PR(Ns+2, 1, i+1), g4=PR(Ns+4, 1, i+1), &
                               F=F(:, i))
      if (Ns>1) then
        if (F(1, i)>0._R_P) then
          F(1:self%Ns, i) = PR(1:Ns, 2, i  )/PR(Ns+3, 2, i  )*F(1, i)
        else
          F(1:self%Ns, i) = PR(1:Ns, 1, i+1)/PR(Ns+3, 1, i+1)*F(1, i)
        endif
      endif
    enddo
    ! compute residuals
    allocate(euler_1D :: dState_dt)
    select type(dState_dt)
    class is(euler_1D)
      dState_dt = self
      do i=1, Ni
        dState_dt%U(:, i) = (F(:, i - 1) - F(:, i)) / self%Dx
      enddo
    endselect
  endassociate
  return
  !---------------------------------------------------------------------------------------------------------------------------------
  endfunction dEuler_dt

All Procedures

a a a a a add_burgers add_euler add_euler add_euler add_lorenz allocate_integrand_members allocate_integrand_members allocate_integrand_members allocate_integrand_members allocate_integrand_members amplitude_phase assign_abstract assign_integrand assign_integrand assign_integrand assign_multistage assign_multistage_multistep assign_multistep assign_real assign_real assign_real average_solution burgers_assign_burgers burgers_assign_real burgers_local_error burgers_multiply_burgers burgers_multiply_real check_error check_scheme_has_fast_mode check_scheme_has_fast_mode check_scheme_has_fast_mode class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name class_name compute_dt compute_dt compute_dt compute_dt compute_dt compute_dt compute_dt compute_dx compute_inter_states compute_inter_states compute_inter_states compute_inter_states compute_inter_states conservative2primitive conservative2primitive conservative2primitive conservative2primitive conservative2primitive d2Burgers_dx2 dBurgers_dt dBurgers_dx description description description description destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy destroy_abstract destroy_multistage destroy_multistage_multistep destroy_multistep destroy_rk destroy_rk dEuler_dt dEuler_dt dEuler_dt dEuler_dt dEuler_dt dLorenz_dt dt_ratio dU_dt dU_dt dU_dt E E E E E error error error euler_assign_euler euler_assign_euler euler_assign_euler euler_assign_euler euler_assign_euler euler_assign_real euler_assign_real euler_assign_real euler_local_error euler_local_error euler_local_error euler_multiply_euler euler_multiply_euler euler_multiply_euler euler_multiply_real euler_multiply_real euler_multiply_real exact_solution exact_solution exact_solution execute execute execute export_tecplot export_tecplot export_tecplot foodie_integrator_class_names foodie_integrator_factory foodie_integrator_schemes H H H H H has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode has_fast_mode impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions impose_boundary_conditions init init init init init init init init init init init init init init_rk init_rk initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize initialize_order_s initialize_order_s_1 integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integr_assign_integr integrand_add_integrand integrand_add_integrand integrand_add_integrand integrand_add_integrand_fast integrand_add_integrand_fast integrand_add_integrand_fast integrand_add_real integrand_add_real integrand_add_real integrand_dimension integrand_dimension integrand_dimension integrand_multiply_integrand integrand_multiply_integrand integrand_multiply_integrand integrand_multiply_integrand_fast integrand_multiply_integrand_fast integrand_multiply_integrand_fast integrand_multiply_real integrand_multiply_real integrand_multiply_real integrand_multiply_real_scalar integrand_multiply_real_scalar integrand_multiply_real_scalar integrand_multiply_real_scalar_fast integrand_multiply_real_scalar_fast integrand_multiply_real_scalar_fast integrand_sub_integrand integrand_sub_integrand integrand_sub_integrand integrand_sub_real integrand_sub_real integrand_sub_real integrand_subtract_integrand_fast integrand_subtract_integrand_fast integrand_subtract_integrand_fast integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_fast integrate_order_2 integrate_order_2_fast integrate_order_3 integrate_order_3_fast integrate_order_s integrate_order_s_1 integrate_order_s_1_fast integrate_order_s_fast integrate_rk integrate_rk is_admissible is_available is_class_available is_multistage is_multistage is_multistage is_multistep is_multistep is_multistep is_scheme_available is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported is_supported local_error local_error local_error lorenz_assign_lorenz lorenz_assign_real lorenz_local_error lorenz_multiply_lorenz lorenz_multiply_real new_Dt observed_order observed_order observed_order omega output output output output output output output output output output p p p p p parse_cli parse_cli parse_cli previous_step previous_step previous_step primitive2conservative primitive2conservative primitive2conservative primitive2conservative primitive2conservative r r r r r real_add_integrand real_add_integrand real_add_integrand real_multiply_burgers real_multiply_euler real_multiply_euler real_multiply_euler real_multiply_integrand real_multiply_integrand real_multiply_integrand real_multiply_lorenz real_scalar_multiply_integrand real_scalar_multiply_integrand real_scalar_multiply_integrand real_sub_integrand real_sub_integrand real_sub_integrand reconstruct_interfaces reconstruct_interfaces_states reconstruct_interfaces_states reconstruct_interfaces_states reconstruct_interfaces_states reconstruct_interfaces_states registers_number riemann_solver riemann_solver riemann_solver riemann_solver riemann_solver save_results save_results save_results save_results save_results save_results save_results save_results save_results save_time_serie save_time_serie save_time_serie save_time_serie save_time_serie scheme_number set_cli set_cli set_cli set_sin_wave_initial_state set_square_wave_initial_state stages_number stages_number stages_number steps_number steps_number steps_number sub_burgers sub_euler sub_euler sub_euler sub_lorenz supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes supported_schemes synchronize synchronize synchronize synchronize t_fast t_fast t_fast test test test_ab test_ab test_ab test_euler test_euler test_euler test_leapfrog test_leapfrog test_leapfrog test_ls_rk test_ls_rk test_ls_rk test_tvd_rk test_tvd_rk test_tvd_rk tokenize trigger_error update_previous update_previous update_previous_steps update_previous_steps update_previous_steps