init_rk Subroutine

private elemental subroutine init_rk(self, stages)

Create the actual RK integrator: initialize the Butcher' table coefficients.

Arguments

Type	Intent	Optional	Attributes		Name
class(tvd_runge_kutta_integrator),	intent(inout)			::	self	RK integrator.
integer(kind=I_P),	intent(in)			::	stages	Number of stages used.

Source Code

init_rk

Source Code

  elemental subroutine init_rk(self, stages)
  !---------------------------------------------------------------------------------------------------------------------------------
  !< Create the actual RK integrator: initialize the Butcher' table coefficients.
  !---------------------------------------------------------------------------------------------------------------------------------
  class(tvd_runge_kutta_integrator), intent(INOUT) :: self   !< RK integrator.
  integer(I_P),                      intent(IN)    :: stages !< Number of stages used.
  !---------------------------------------------------------------------------------------------------------------------------------

  !---------------------------------------------------------------------------------------------------------------------------------
  if (stages<1) return ! error print should be added
  self%stages = stages
  if (allocated(self%beta)) deallocate(self%beta) ; allocate(self%beta(1:stages          )) ; self%beta = 0._R_P
  if (allocated(self%alph)) deallocate(self%alph) ; allocate(self%alph(1:stages, 1:stages)) ; self%alph = 0._R_P
  if (allocated(self%gamm)) deallocate(self%gamm) ; allocate(self%gamm(          1:stages)) ; self%gamm = 0._R_P
  select case(stages)
  case(1)
    ! RK(1,1) Forward-Euler
    self%beta(1) = 1._R_P
  case(2)
    ! SSPRK(2,2)
    self%beta(1) = 0.5_R_P
    self%beta(2) = 0.5_R_P

    self%alph(2, 1) = 1._R_P

    self%gamm(2) = 1._R_P
  case(3)
    ! SSPRK(3,3)
    self%beta(1) = 1._R_P/6._R_P
    self%beta(2) = 1._R_P/6._R_P
    self%beta(3) = 2._R_P/3._R_P

    self%alph(2, 1) = 1._R_P
    self%alph(3, 1) = 0.25_R_P ; self%alph(3, 2) = 0.25_R_P

    self%gamm(2) = 1._R_P
    self%gamm(3) = 0.5_R_P
  case(5)
    ! SSPRK(5,4)
    self%beta(1) = 0.14681187618661_R_P
    self%beta(2) = 0.24848290924556_R_P
    self%beta(3) = 0.10425883036650_R_P
    self%beta(4) = 0.27443890091960_R_P
    self%beta(5) = 0.22600748319395_R_P

    self%alph(2, 1)=0.39175222700392_R_P
    self%alph(3, 1)=0.21766909633821_R_P;self%alph(3, 2)=0.36841059262959_R_P
    self%alph(4, 1)=0.08269208670950_R_P;self%alph(4, 2)=0.13995850206999_R_P;self%alph(4, 3)=0.25189177424738_R_P
    self%alph(5, 1)=0.06796628370320_R_P;self%alph(5, 2)=0.11503469844438_R_P;self%alph(5, 3)=0.20703489864929_R_P
    self%alph(5, 4)=0.54497475021237_R_P

    self%gamm(2) = 0.39175222700392_R_P
    self%gamm(3) = 0.58607968896780_R_P
    self%gamm(4) = 0.47454236302687_R_P
    self%gamm(5) = 0.93501063100924_R_P
  endselect
  return
  !---------------------------------------------------------------------------------------------------------------------------------
  endsubroutine init_rk

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