riemann_solver Subroutine

private pure subroutine riemann_solver(self, p1, r1, u1, g1, p4, r4, u4, g4, F)

Solve the Riemann problem between the state $1$ and $4$ using the (local) Lax Friedrichs (Rusanov) solver.

Arguments

Type	Intent		Name
class(euler_1D),	intent(in)	::	self	Euler field.
real(kind=R_P),	intent(in)	::	p1	Pressure of state 1.
real(kind=R_P),	intent(in)	::	r1	Density of state 1.
real(kind=R_P),	intent(in)	::	u1	Velocity of state 1.
real(kind=R_P),	intent(in)	::	g1	Specific heats ratio of state 1.
real(kind=R_P),	intent(in)	::	p4	Pressure of state 4.
real(kind=R_P),	intent(in)	::	r4	Density of state 4.
real(kind=R_P),	intent(in)	::	u4	Velocity of state 4.
real(kind=R_P),	intent(in)	::	g4	Specific heats ratio of state 4.
real(kind=R_P),	intent(out)	::	F(1:self%Nc)	Resulting fluxes.

Calls

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Source Code

riemann_solver

Source Code

  pure subroutine riemann_solver(self, p1, r1, u1, g1, p4, r4, u4, g4, F)
  !---------------------------------------------------------------------------------------------------------------------------------
  !< Solve the Riemann problem between the state $1$ and $4$ using the (local) Lax Friedrichs (Rusanov) solver.
  !---------------------------------------------------------------------------------------------------------------------------------
  class(euler_1D), intent(IN)  :: self         !< Euler field.
  real(R_P),       intent(IN)  :: p1           !< Pressure of state 1.
  real(R_P),       intent(IN)  :: r1           !< Density of state 1.
  real(R_P),       intent(IN)  :: u1           !< Velocity of state 1.
  real(R_P),       intent(IN)  :: g1           !< Specific heats ratio of state 1.
  real(R_P),       intent(IN)  :: p4           !< Pressure of state 4.
  real(R_P),       intent(IN)  :: r4           !< Density of state 4.
  real(R_P),       intent(IN)  :: u4           !< Velocity of state 4.
  real(R_P),       intent(IN)  :: g4           !< Specific heats ratio of state 4.
  real(R_P),       intent(OUT) :: F(1:self%Nc) !< Resulting fluxes.
  real(R_P)                    :: F1(1:3)      !< State 1 fluxes.
  real(R_P)                    :: F4(1:3)      !< State 4 fluxes.
  real(R_P)                    :: u            !< Velocity of the intermediate states.
  real(R_P)                    :: p            !< Pressure of the intermediate states.
  real(R_P)                    :: S1           !< Maximum wave speed of state 1 and 4.
  real(R_P)                    :: S4           !< Maximum wave speed of state 1 and 4.
  real(R_P)                    :: lmax         !< Maximum wave speed estimation.
  !---------------------------------------------------------------------------------------------------------------------------------

  !---------------------------------------------------------------------------------------------------------------------------------
  ! evaluating the intermediates states 2 and 3 from the known states U1,U4 using the PVRS approximation
  call compute_inter_states(p1 = p1, r1 = r1, u1 = u1, g1 = g1, p4 = p4, r4 = r4, u4 = u4, g4 = g4, p = p, S = u, S1 = S1, S4 = S4)
  ! evalutaing the maximum waves speed
  lmax = max(abs(S1), abs(u), abs(S4))
  ! computing the fluxes of state 1 and 4
  F1 = fluxes(p = p1, r = r1, u = u1, g = g1)
  F4 = fluxes(p = p4, r = r4, u = u4, g = g4)
  ! computing the Lax-Friedrichs fluxes approximation
  F(1)         = 0.5_R_P*(F1(1) + F4(1) - lmax*(r4                        - r1                       ))
  F(self%Ns+1) = 0.5_R_P*(F1(2) + F4(2) - lmax*(r4*u4                     - r1*u1                    ))
  F(self%Ns+2) = 0.5_R_P*(F1(3) + F4(3) - lmax*(r4*E(p=p4,r=r4,u=u4,g=g4) - r1*E(p=p1,r=r1,u=u1,g=g1)))
  return
  !---------------------------------------------------------------------------------------------------------------------------------
  contains
    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

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