r Function

  1. type_euler-1D-openmp.f90
  2. type_euler_1D_openmp
  3. r

private elemental function r(p, a, g) result(density)

Compute the density for an ideal calorically perfect gas.

Arguments

Type IntentOptional AttributesName
real(kind=R_P), intent(in) :: p

Pressure.
real(kind=R_P), intent(in) :: a

Speed of sound.
real(kind=R_P), intent(in) :: g

Specific heats ratio \(\frac{{c_p}}{{c_v}}\).

Return Value real(kind=R_P)

Density.


Source Code

r

Source Code

    pure function fluxes(p, r, u, g) result(Fc)
    !-------------------------------------------------------------------------------------------------------------------------------
    !< 1D Euler fluxes from primitive variables.
    !-------------------------------------------------------------------------------------------------------------------------------
    real(R_P), intent(IN) :: p       !< Pressure.
    real(R_P), intent(IN) :: r       !< Density.
    real(R_P), intent(IN) :: u       !< Velocity.
    real(R_P), intent(IN) :: g       !< Specific heats ratio.
    real(R_P)             :: Fc(1:3) !< State fluxes.
    !-------------------------------------------------------------------------------------------------------------------------------

    !-------------------------------------------------------------------------------------------------------------------------------
    Fc(1) = r*u
    Fc(2) = Fc(1)*u + p
    Fc(3) = Fc(1)*H(p=p, r=r, u=u, g=g)
    return
    !-------------------------------------------------------------------------------------------------------------------------------
    endfunction fluxes
  endsubroutine riemann_solver

  ! non type-bound procedures
  pure subroutine compute_inter_states(r1, p1, u1, g1, r4, p4, u4, g4, p, S, S1, S4)
  !------------------------------------------------------------------------------------------------------------------------------
  !< Compute inter states (23*-states) from state1 and state4.
  !------------------------------------------------------------------------------------------------------------------------------
  real(R_P), intent(IN)  :: r1             !< Density of state 1.
  real(R_P), intent(IN)  :: p1             !< Pressure of state 1.
  real(R_P), intent(IN)  :: u1             !< Velocity of state 1.
  real(R_P), intent(IN)  :: g1             !< Specific heat ratio of state 1.
  real(R_P), intent(IN)  :: r4             !< Density of state 4.
  real(R_P), intent(IN)  :: p4             !< Pressure of state 4.
  real(R_P), intent(IN)  :: u4             !< Velocity of state 4.
  real(R_P), intent(IN)  :: g4             !< Specific heat ratio of state 4.
  real(R_P), intent(OUT) :: p              !< Pressure of the intermediate states.
  real(R_P), intent(OUT) :: S              !< Contact discontinuity signal velocity.
  real(R_P), intent(OUT) :: S1             !< Left fastest signal velocity.
  real(R_P), intent(OUT) :: S4             !< Right fastest signal velocity.
  real(R_P)              :: a1             !< Speed of sound of state 1.
  real(R_P)              :: a4             !< Speed of sound of state 4.
  real(R_P)              :: ram            !< Mean value of rho*a.
  real(R_P), parameter   :: toll=1e-10_R_P !< Tollerance.
  !------------------------------------------------------------------------------------------------------------------------------

  !------------------------------------------------------------------------------------------------------------------------------
  ! evaluation of the intermediate states pressure and velocity
  a1  = sqrt(g1 * p1 / r1)                              ! left speed of sound
  a4  = sqrt(g4 * p4 / r4)                              ! right speed of sound
  ram = 0.5_R_P * (r1 + r4) * 0.5_R_P * (a1 + a4)       ! product of mean density for mean speed of sound
  S   = 0.5_R_P * (u1 + u4) - 0.5_R_P * (p4 - p1) / ram ! evaluation of the contact wave speed (velocity of intermediate states)
  p   = 0.5_R_P * (p1 + p4) - 0.5_R_P * (u4 - u1) * ram ! evaluation of the pressure of the intermediate states
  ! evaluation of the left wave speeds
  if (p<=p1*(1._R_P + toll)) then
    ! rarefaction
    S1 = u1 - a1
  else
    ! shock
    S1 = u1 - a1 * sqrt(1._R_P + (g1 + 1._R_P) / (2._R_P * g1) * (p / p1 - 1._R_P))
  endif
  ! evaluation of the right wave speeds
  if (p<=p4 * (1._R_P + toll)) then
    ! rarefaction
    S4 = u4 + a4
  else
    ! shock
    S4 = u4 + a4 * sqrt(1._R_P + (g4 + 1._R_P) / (2._R_P * g4) * ( p / p4 - 1._R_P))
  endif
  return
  !------------------------------------------------------------------------------------------------------------------------------
  endsubroutine compute_inter_states

  elemental function p(r, a, g) result(pressure)
  !---------------------------------------------------------------------------------------------------------------------------------
  !< Compute the pressure for an ideal calorically perfect gas.
  !---------------------------------------------------------------------------------------------------------------------------------
  real(R_P), intent(IN) :: r        !< Density.
  real(R_P), intent(IN) :: a        !< Speed of sound.
  real(R_P), intent(IN) :: g        !< Specific heats ratio \(\frac{{c_p}}{{c_v}}\).
  real(R_P)             :: pressure !< Pressure.
  !---------------------------------------------------------------------------------------------------------------------------------

  !---------------------------------------------------------------------------------------------------------------------------------
  pressure = r*a*a/g
  return
  !---------------------------------------------------------------------------------------------------------------------------------
  endfunction p

  elemental function r(p, a, g) result(density)
  !---------------------------------------------------------------------------------------------------------------------------------
  !< Compute the density for an ideal calorically perfect gas.
  !---------------------------------------------------------------------------------------------------------------------------------
  real(R_P), intent(IN) :: p       !< Pressure.
  real(R_P), intent(IN) :: a       !< Speed of sound.
  real(R_P), intent(IN) :: g       !< Specific heats ratio \(\frac{{c_p}}{{c_v}}\).
  real(R_P)             :: density !< Density.
  !---------------------------------------------------------------------------------------------------------------------------------

  !---------------------------------------------------------------------------------------------------------------------------------
  density = g*p/(a*a)
  return
  !---------------------------------------------------------------------------------------------------------------------------------
  endfunction r

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