lib_He_thermo_m

Helium equation of state (Arp reference EOS) and transport properties.

Uses

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Used by

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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Variables

Type	Visibility	Attributes		Name		Initial
integer,	public,	parameter	::	Pri_ro	=	1	Density
integer,	public,	parameter	::	Pri_u	=	2	Velocity
integer,	public,	parameter	::	Pri_p	=	3	Pressure
integer,	public,	parameter	::	Pri_e	=	4	Internal energy
integer,	public,	parameter	::	Pri_T	=	5	Temperature
integer,	public,	parameter	::	Pri_c	=	6	Sound speed
integer,	public,	parameter	::	Pri_R	=	7	Extra variable for the mechanical equilibrium recovering
integer,	public,	parameter	::	Con_Mas	=	1	Mass conservative variable
integer,	public,	parameter	::	Con_Qdm	=	2	Momentum conservative variable
integer,	public,	parameter	::	Con_Ene	=	3	Energy conservative variable
integer,	public,	parameter	::	Con_R	=	4	Extra variable for conservative variable array
real(kind=dp),	public,	parameter	::	T_He_min	=	3.0_dp	EOS lower bound (K)
real(kind=dp),	public,	parameter	::	T_He_max	=	1500.0_dp	EOS upper bound (K)
real(kind=dp),	public,	parameter	::	MolMass	=	4.0026e-3_dp	Molar mass of helium (kg/mol)
real(kind=dp),	public,	parameter	::	R_cte_gaz_Arp	=	8.31431e-3_dp	Universal gas constant (kJ/(mol*K))
real(kind=dp),	public,	parameter	::	cp0_Arp	=	5193.16943986d0MolMass1.0e-3_dp	Reference specific heat at constant pressure (kJ/(kg*K))
real(kind=dp),	private,	parameter	::	tau	=	1.0_dp/(17.399_dp**2)
real(kind=dp),	private,	parameter	::	q0_Arp	=	5210.521090595d0MolMass1.0e-3_dp
real(kind=dp),	private,	parameter	::	nn(32)	=	[+0.4558980227431e-04_dp, 0.1260692007853e-02_dp, -0.7139657549318e-02_dp, +0.9728903861441e-02_dp, -0.1589302471562e-01_dp, 0.1454229259623e-05_dp, -0.4708238429298e-04_dp, 0.1132915223587e-02_dp, 0.2410763742104e-02_dp, -0.5093547838381e-08_dp, 0.2699726927900e-05_dp, -0.3954146691114e-04_dp, +0.1551961438127e-08_dp, 0.1050712335785e-07_dp, -0.5501158366750e-07_dp, -0.1037673478521e-09_dp, 0.6446881346448e-12_dp, 0.3298960057071e-10_dp, -0.3555585738784e-12_dp, -0.6885401367690e-02_dp, 0.9166109232806e-02_dp, -0.6544314242937e-05_dp, -0.3315398880031e-04_dp, -0.2067693644676e-07_dp, +0.3850153114958e-07_dp, -0.1399040626999e-10_dp, -0.1888462892389e-11_dp, -0.4595138561035e-14_dp, 0.6872567403738e-14_dp, -0.6097223119177e-18_dp, -0.7636186157005e-17_dp, 0.3848665703556e-17_dp]
real(kind=dp),	private,	parameter	::	Newton_T_guess0	=	10.0_dp
real(kind=dp),	private,	parameter	::	Newton_FunctTol	=	1.0e-8_dp
integer,	private,	parameter	::	Newton_MaxIte	=	80
real(kind=dp),	private,	parameter	::	Brent_MachEps	=	1.0e-15_dp
real(kind=dp),	private,	parameter	::	Brent_Tol	=	1.0e-10_dp
real(kind=dp),	private,	parameter	::	Brent_ResidTol	=	Newton_FunctTol
real(kind=dp),	private,	parameter	::	ro_from_pT_min_Arp	=	0.01_dp/(MolMass*1000.0_dp)
real(kind=dp),	private,	parameter	::	ro_from_pT_max_Arp	=	290.0_dp/(MolMass*1000.0_dp)

Derived Types

type, private :: ThArrays_t

Components

Type	Visibility	Attributes		Name
real(kind=dp),	public,	dimension(14)	::	f
real(kind=dp),	public,	dimension(14)	::	g
real(kind=dp),	public,	dimension(14)	::	Derf
real(kind=dp),	public,	dimension(14)	::	Derg
real(kind=dp),	public,	dimension(14)	::	Dergg
real(kind=dp),	public,	dimension(14)	::	hh
real(kind=dp),	public,	dimension(14)	::	Derhh
real(kind=dp),	public,	dimension(14)	::	Der2f
real(kind=dp),	public,	dimension(14)	::	Der2g
real(kind=dp),	public,	dimension(14)	::	Der2gg
real(kind=dp),	public,	dimension(14)	::	gg
real(kind=dp),	public,	dimension(14)	::	ff

type, private, extends(brent_t) :: ro_from_pT_obj_t

Components

Type	Visibility	Attributes		Name		Initial
real(kind=dp),	public		::	p
real(kind=dp),	public		::	T

Type-Bound Procedures

procedure, public :: f => funct_ro_from_pT

type, private, extends(brent_t) :: T_from_roP_obj_t

Components

Type	Visibility	Attributes		Name		Initial
real(kind=dp),	public		::	ro
real(kind=dp),	public		::	p

Type-Bound Procedures

procedure, public :: f => funct_T_from_roP

type, private, extends(brent_t) :: T_from_roE_obj_t

Components

Type	Visibility	Attributes		Name		Initial
real(kind=dp),	public		::	ro
real(kind=dp),	public		::	e

Type-Bound Procedures

procedure, public :: f => funct_T_from_roE

Functions

private function funct_ro_from_pT(me, x)

Arguments

Type	Intent	Optional	Attributes		Name
class(ro_from_pT_obj_t),	intent(in)			::	me
real(kind=dp),	intent(in)			::	x	x is ro (Arp units)

Return Value real(kind=dp)

private function funct_T_from_roP(me, x)

Arguments

Type	Intent	Optional	Attributes		Name
class(T_from_roP_obj_t),	intent(in)			::	me
real(kind=dp),	intent(in)			::	x	x is T

Return Value real(kind=dp)

private function funct_T_from_roE(me, x)

Arguments

Type	Intent	Optional	Attributes		Name
class(T_from_roE_obj_t),	intent(in)			::	me
real(kind=dp),	intent(in)			::	x	x is T

Return Value real(kind=dp)

private function brent(obj, xmin, xmax, label) result(x)

Arguments

Type	Intent		Name
class(brent_t),	intent(in)	::	obj
real(kind=dp),	intent(in)	::	xmin
real(kind=dp),	intent(in)	::	xmax
character(len=*),	intent(in)	::	label

Return Value real(kind=dp)

public elemental function r_roT(ro, T) result(r)

r = rho*h consistent with (ro,T), fast direct evaluation

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	ro
real(kind=dp),	intent(in)			::	T

Return Value real(kind=dp)

public function ro_pT(p, T) result(ro)

Solve p(ro,T) = p for ro.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	p
real(kind=dp),	intent(in)			::	T

Return Value real(kind=dp)

public function T_roP(ro, p) result(T)

Solve p(ro,T) = p for T.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	ro
real(kind=dp),	intent(in)			::	p

Return Value real(kind=dp)

public function T_roE(ro, e) result(T)

Solve e(ro,T) = e for T

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	ro
real(kind=dp),	intent(in)			::	e

Return Value real(kind=dp)

public function droeint_droP(ro, p, e, dedv, dedp) result(droeint_dro)

Energy-related terms from (ro,p): returns d(rho*e)/d(ro)|p and can also provide e, de/dv|p, and de/dp|v.

Arguments

Type	Intent	Optional		Name
real(kind=dp),	intent(in)		::	ro
real(kind=dp),	intent(in)		::	p
real(kind=dp),	intent(out),	optional	::	e
real(kind=dp),	intent(out),	optional	::	dedv
real(kind=dp),	intent(out),	optional	::	dedp

Return Value real(kind=dp)

Subroutines

private elemental subroutine fill_f_terms(ro, ThAr)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	ro
type(ThArrays_t),	intent(inout)			::	ThAr

private elemental subroutine fill_ff_terms(ro, ThAr)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	ro
type(ThArrays_t),	intent(inout)			::	ThAr

private elemental subroutine fill_g_Dreg_terms(T, ThAr)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	T
type(ThArrays_t),	intent(inout)			::	ThAr

private elemental subroutine eos_pT_terms(ro, T, ThAr)

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	T
type(ThArrays_t),	intent(inout)	::	ThAr

private elemental subroutine fill_e_Tpart(T, ThAr)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	T
type(ThArrays_t),	intent(inout)			::	ThAr

private elemental subroutine eos_e_terms(ro, T, ThAr)

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	T
type(ThArrays_t),	intent(inout)	::	ThAr

private elemental subroutine eos_terms(ro, T, ThAr)

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	T
type(ThArrays_t),	intent(out)	::	ThAr

public elemental subroutine state_roT(ro, T, r, p, e, c)

Full state from (ro,T): r, p, e, c.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	T
real(kind=dp),	intent(out)	::	r
real(kind=dp),	intent(out)	::	p
real(kind=dp),	intent(out)	::	e
real(kind=dp),	intent(out)	::	c

public subroutine state_roP(ro, p, r, e, T, c)

Full state from (ro,p): r, e, T, c. Solves for T internally.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	p
real(kind=dp),	intent(out)	::	r
real(kind=dp),	intent(out)	::	e
real(kind=dp),	intent(out)	::	T
real(kind=dp),	intent(out)	::	c

public subroutine state_roP_withR(ro, p, r, e, T, c)

State from (ro,p) when r is already known (e.g. carried as a conservative variable): e, T, c. Solves for T internally.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	p
real(kind=dp),	intent(in)	::	r
real(kind=dp),	intent(out)	::	e
real(kind=dp),	intent(out)	::	T
real(kind=dp),	intent(out)	::	c

public subroutine state_roE(ro, e, p, T, c)

State from (ro,e): p, T, c for the physical EOS path.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	e
real(kind=dp),	intent(out)	::	p
real(kind=dp),	intent(out)	::	T
real(kind=dp),	intent(out)	::	c

public subroutine state_roE_withR(ro, e, r, p, T, c)

State from (ro,e) when r is already known: p, T, c.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	e
real(kind=dp),	intent(in)	::	r
real(kind=dp),	intent(out)	::	p
real(kind=dp),	intent(out)	::	T
real(kind=dp),	intent(out)	::	c

public elemental subroutine jacobian_roT(ro, T, cv, dPdT, dTdP, dTdRo, dRdRo, dRdT, r, p, d2TdP_dT, d2TdP_dRo)

Arguments

Type	Intent	Optional		Name
real(kind=dp),	intent(in)		::	ro
real(kind=dp),	intent(in)		::	T
real(kind=dp),	intent(out)		::	cv
real(kind=dp),	intent(out)		::	dPdT
real(kind=dp),	intent(out),	optional	::	dTdP
real(kind=dp),	intent(out),	optional	::	dTdRo
real(kind=dp),	intent(out),	optional	::	dRdRo
real(kind=dp),	intent(out),	optional	::	dRdT
real(kind=dp),	intent(out),	optional	::	r
real(kind=dp),	intent(out),	optional	::	p
real(kind=dp),	intent(out),	optional	::	d2TdP_dT
real(kind=dp),	intent(out),	optional	::	d2TdP_dRo

public elemental subroutine dc2_roT(ro, T, dc2dRo, dc2dP)

d(c^2)/dRo and d(c^2)/dP at constant T / constant Ro respectively.

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	T
real(kind=dp),	intent(out)	::	dc2dRo
real(kind=dp),	intent(out)	::	dc2dP

public subroutine he_prop(ro, T, cv, cp, mu, lambda, dPdT)

Viscosity and thermal conductivity correlations for helium. The critical-region enhancement term in lambda needs dP/dRo and dP/dT;

Arguments

Type	Intent		Name
real(kind=dp),	intent(in)	::	ro
real(kind=dp),	intent(in)	::	T
real(kind=dp),	intent(out)	::	cv
real(kind=dp),	intent(out)	::	cp
real(kind=dp),	intent(out)	::	mu
real(kind=dp),	intent(out)	::	lambda
real(kind=dp),	intent(out)	::	dPdT

lib_He_thermo_m Module

Contents

Variables

Derived Types

Functions

Subroutines

Uses

Used by

Variables

Derived Types

type, private :: ThArrays_t

Components

type, private, extends(brent_t) :: ro_from_pT_obj_t

Components

Type-Bound Procedures

type, private, extends(brent_t) :: T_from_roP_obj_t

Components

Type-Bound Procedures

type, private, extends(brent_t) :: T_from_roE_obj_t

Components

Type-Bound Procedures

Functions

private function funct_ro_from_pT(me, x)

Arguments

Return Value real(kind=dp)

private function funct_T_from_roP(me, x)

Arguments

Return Value real(kind=dp)

private function funct_T_from_roE(me, x)

Arguments

Return Value real(kind=dp)

private function brent(obj, xmin, xmax, label) result(x)

Arguments

Return Value real(kind=dp)

public elemental function r_roT(ro, T) result(r)

Arguments

Return Value real(kind=dp)

public function ro_pT(p, T) result(ro)

Arguments

Return Value real(kind=dp)

public function T_roP(ro, p) result(T)

Arguments

Return Value real(kind=dp)

public function T_roE(ro, e) result(T)

Arguments

Return Value real(kind=dp)

public function droeint_droP(ro, p, e, dedv, dedp) result(droeint_dro)

Arguments

Return Value real(kind=dp)

Subroutines

private elemental subroutine fill_f_terms(ro, ThAr)

Arguments

private elemental subroutine fill_ff_terms(ro, ThAr)

Arguments

private elemental subroutine fill_g_Dreg_terms(T, ThAr)

Arguments

private elemental subroutine eos_pT_terms(ro, T, ThAr)

Arguments

private elemental subroutine fill_e_Tpart(T, ThAr)

Arguments

private elemental subroutine eos_e_terms(ro, T, ThAr)

Arguments

private elemental subroutine eos_terms(ro, T, ThAr)

Arguments

public elemental subroutine state_roT(ro, T, r, p, e, c)

Arguments

public subroutine state_roP(ro, p, r, e, T, c)

Arguments

public subroutine state_roP_withR(ro, p, r, e, T, c)

Arguments

public subroutine state_roE(ro, e, p, T, c)

Arguments

public subroutine state_roE_withR(ro, e, r, p, T, c)

Arguments

public elemental subroutine jacobian_roT(ro, T, cv, dPdT, dTdP, dTdRo, dRdRo, dRdT, r, p, d2TdP_dT, d2TdP_dRo)

Arguments

public elemental subroutine dc2_roT(ro, T, dc2dRo, dc2dP)

Arguments

public subroutine he_prop(ro, T, cv, cp, mu, lambda, dPdT)

Arguments