Time discretization

Routines relative to time discretization of PDEs. More...

Namespaces
module	enum_flux_limiter
	Time order discrezation enumeration.
module	enum_refined_velocity_method
	Time order discrezation enumeration.
module	enum_time_order_discretization
	Time order discrezation enumeration.
module	variables_time_discretization
	Declaration of variables associated to the time discretization.

Functions
subroutine	mod_compute_time_coefficients::compute_time_coefficients (time_order_discretization, time_step, time_step_n, time_discretization_coef_np1, time_discretization_coef_n, time_discretization_coef_nm1)
	Compute the time coefficients of the temporal scheme of a PDE.
subroutine	compute_time_loop_cfl ()
	Compute time steps that fulfill a multiple of the CFL.
double precision function	mod_compute_time_step_cfl_advection::compute_time_step_cfl_advection (velocity, temporal_stability_factor)
	Compute the time step restricted by the CFL Warning: this is called "advection" refering the the mathematical advection equation Thus we look for the maximum velocity in the whole domain.
double precision function	mod_compute_time_step_cfl_advection::compute_cfl_p_step_advection (velocity, time_step_local)
	Compute the time step restricted by the CFL for direction splitted advection Warning: this is called "advection" refering the the mathematical advection equation Thus we look for the maximum velocity in the whole domain.
double precision function	mod_compute_time_step_cfl_advection::compute_cfl_acoustic (speed_of_sound, time_step_local)
	Compute the acoustic CFL.
double precision function	mod_compute_time_step_cfl_advection::compute_time_step_cfl_acoustic (speed_of_sound, temporal_stability_factor)
	Compute the time_step related to acoustic CFL.
double precision function	mod_compute_time_step_cfl_advection_surface_tension::compute_time_step_cfl_advection_surface_tension (velocity, density, temporal_stability_factor)
	Compute the time step restricted by the CFL Warning: this is called "advection" referring the the mathematical advection equation Thus we look for the maximum velocity plus the maximum capillary velocity (surface tension) in the whole domain.
double precision function	mod_compute_time_step_cfl_advection_surface_tension::compute_time_step_cfl_advection_1d_surface_tension (velocity, density, temporal_stability_factor)
	Compute the time step restricted by the CFL Warning: this is called "advection" referring the the mathematical advection equation Thus we look for the maximum velocity in the whole domain.
subroutine	stop_tests ()
	Stops simulation when a stop tests is satisfied.
subroutine	time_step_switch ()
	Switch time dependant variables to next time step.

Detailed Description

Routines relative to time discretization of PDEs.

The reader willl find in this directory routines to:

• compute time step as a multiple of the CFL (time_loop_cfl.f90)
• stop the simulation if some stop tests are satisfied (stop_tests.f90)
• assign field values defined at \( t^{n+1} \) to field values defined at \( t^{n} \) (time_step_switch.f90)
• compute the time coefficients of the temporal scheme of a PDE ('compite_time_coefficients.f90')

The file variables.f90 contains the declaration of scalar variables associated to time discretization, and enum.f90 the enumarations.

Function Documentation

compute_cfl_acoustic()

double precision function mod_compute_time_step_cfl_advection::compute_cfl_acoustic	(	double precision, dimension(:,:,:), intent(in), allocatable	speed_of_sound,
		double precision, intent(in)	time_step_local )

Compute the acoustic CFL.

Parameters

[in]	speed_of_sound	the speed_of_sound field
[in]	time_step_local	current time step

Returns

the time_step

compute_cfl_p_step_advection()

double precision function mod_compute_time_step_cfl_advection::compute_cfl_p_step_advection	(	type(t_face_field), intent(in)	velocity,
		double precision, intent(in)	time_step_local )

Compute the time step restricted by the CFL for direction splitted advection Warning: this is called "advection" refering the the mathematical advection equation Thus we look for the maximum velocity in the whole domain.

Parameters

[in]	velocity	the velocity field
[in]	time_step_local	current time step

Returns

the time_step

compute_time_coefficients()

subroutine mod_compute_time_coefficients::compute_time_coefficients	(	integer, intent(in)	time_order_discretization,
		double precision, intent(in)	time_step,
		double precision, intent(in)	time_step_n,
		double precision, intent(out)	time_discretization_coef_np1,
		double precision, intent(out)	time_discretization_coef_n,
		double precision, intent(out)	time_discretization_coef_nm1 )

Compute the time coefficients of the temporal scheme of a PDE.

This temporal term is written as follow:

∂φ/∂t ≈ α φⁿ⁺¹ + β φⁿ + γ φⁿ⁻¹

• 1ˢᵗ order Euler scheme:

    1           -1
  

  α = ----— β = ----— γ = 0 Δtⁿ⁺¹ Δtⁿ⁺¹
• 2ⁿᵈ order Backward Differentiation Formula:

    2Δtⁿ⁺¹ + Δtⁿ           -(Δtⁿ⁺¹ + Δtⁿ)             Δtⁿ⁺¹
  

  α = ---------------— β = -------------— γ = -------------— Δtⁿ⁺¹(Δtⁿ⁺¹+Δtⁿ) Δtⁿ⁺¹Δtⁿ Δtⁿ(Δtⁿ⁺¹+Δtⁿ)

compute_time_loop_cfl()

subroutine compute_time_loop_cfl

Compute time steps that fulfill a multiple of the CFL.

This routine computes the time step that is equal to a multiple of the CFL.

This routine computes phase_advection_time_step, energy_time_step, navier_time_step equal to CFL*temporal_stability_factor

compute_time_step_cfl_acoustic()

double precision function mod_compute_time_step_cfl_advection::compute_time_step_cfl_acoustic	(	double precision, dimension(:,:,:), intent(in), allocatable	speed_of_sound,
		double precision, intent(in)	temporal_stability_factor )

Compute the time_step related to acoustic CFL.

Parameters

[in]	speed_of_sound	the velocity field
[in]	temporal_stability_factor	the coefficient multiplying the maximum time step

Returns

the time_step

compute_time_step_cfl_advection()

double precision function mod_compute_time_step_cfl_advection::compute_time_step_cfl_advection	(	type(t_face_field), intent(in)	velocity,
		double precision, intent(in)	temporal_stability_factor )

Compute the time step restricted by the CFL Warning: this is called "advection" refering the the mathematical advection equation Thus we look for the maximum velocity in the whole domain.

Parameters

[in]	velocity	the velocity field
[in]	temporal_stability_factor	the coefficient multiplying the maximum time step

Returns

the time_step

compute_time_step_cfl_advection_1d_surface_tension()

double precision function mod_compute_time_step_cfl_advection_surface_tension::compute_time_step_cfl_advection_1d_surface_tension	(	type(t_face_field), intent(in)	velocity,
		double precision, dimension(:,:,:), intent(in)	density,
		double precision, intent(in)	temporal_stability_factor )

Compute the time step restricted by the CFL Warning: this is called "advection" referring the the mathematical advection equation Thus we look for the maximum velocity in the whole domain.

Parameters

[in]	velocity	the velocity field
[in]	density	the density field
[in]	temporal_stability_factor	the coefficient multiplying the maximum time step

Returns

the time_step

compute_time_step_cfl_advection_surface_tension()

double precision function mod_compute_time_step_cfl_advection_surface_tension::compute_time_step_cfl_advection_surface_tension	(	type(t_face_field), intent(in)	velocity,
		double precision, dimension(:,:,:), intent(in)	density,
		double precision, intent(in)	temporal_stability_factor )

Compute the time step restricted by the CFL Warning: this is called "advection" referring the the mathematical advection equation Thus we look for the maximum velocity plus the maximum capillary velocity (surface tension) in the whole domain.

Parameters

[in]	velocity	the velocity field
[in]	density	the density field
[in]	temporal_stability_factor	the coefficient multiplying the maximum time step

Returns

the time_step

stop_tests()

subroutine stop_tests

Stops simulation when a stop tests is satisfied.

The stop tests are based on:

• ellapsed time;
• the stationarity of the velocity, temperature, species concentration, and divergence fields, with respect to a tolerance value.

When all stop tests are satisfied, is_stop_simulation is set to .true. and the simulation is ended.

time_step_switch()

subroutine time_step_switch

Switch time dependant variables to next time step.

This routine switches time dependant variable defined at \(t^{n}\) to their value at \( t^{n+1} \). If second order time is used, switch is done between \(t^{n}\) and \(t^{n-1}\).