Collaboration diagram for Time stepping:

Variables
integer, save	ischtp
	time order of time stepping

integer, save	istmpf
	time order of the mass flux scheme The chosen value for istmpf will automatically determine the value given to the variable thetfl.

integer(c_int), pointer, save	nterup
	number of interations on the pressure-velocity coupling on Navier-Stokes (for the PISO algorithm)

integer, save	isno2t
	isno2t specifies the time scheme activated for the source terms of the momentum equation, apart from convection and diffusion (for instance: head loss, transposed gradient, ...).

integer, save	isto2t
	isto2t specifies the time scheme activated for the source terms of the turbulence equations i.e. related to , $R_{ij}$ , $\varepsilon$ , $\omega$ , $\varphi$ , $\overline{f}$ ), apart from convection and diffusion.

integer, dimension(nscamx), save	isso2t
	for each scalar, isso2t specifies the time scheme activated for the source terms of the equation for the scalar, apart from convection and diffusion (for instance: variance production, user-specified terms, ...).

integer, save	initvi
	initvi : =1 if total viscosity read from checkpoint file

integer, save	initro
	initro : =1 if density read from checkpoint file

integer, save	initcp
	initcp : =1 if specific heat read from checkpoint file

integer, dimension(nscamx), save	initvs
	initvs : =1 if scalar diffusivity read from checkpoint file

double precision, save	thetsn
	$\theta_S$ -scheme for the source terms in the Navier-Stokes equations when the source term extrapolation has been activated (see isno2t), following the formula $(S_e)^{n+\theta}=(1+\theta)S_e^n-\theta S_e^{n-1}$ . The value of = thetsn is deduced from the value chosen for isno2t. Generally only the value 0.5 is used.

double precision, save	thetst
	$\theta$ -scheme for the extrapolation of the nonlinear explicit source terms $S_e$ of the turbulence equations when the source term extrapolation has been activated (see isto2t), following the formula $(S_e)^{n+\theta}=(1+\theta)S_e^n-\theta S_e^{n-1}$ . The value of is deduced from the value chosen for isto2t. Generally, only the value 0.5 is used.

double precision, dimension(nscamx), save	thetss
	$\theta$ -scheme for the extrapolation of the nonlinear explicit source term of the scalar transport equation when the source term extrapolation has been activated (see isso2t), following the formula $(S_e)^{n+\theta}=(1+\theta)S_e^n-\theta S_e^{n-1}$ . The value of $\theta$ = thetss is deduced from the value chosen for isso2t. Generally, only the value 0.5 is used.

double precision, save	thetfl
	$\theta$ -scheme for the mass flux when a second-order time scheme has been activated for the mass flow (see istmpf).

double precision, save	thetvi
	$\theta$ -scheme for the extrapolation of the physical property $\phi$ "total viscosity" when the extrapolation has been activated (see time_extrapolated key word), according to the formula $\phi^{n+\theta}=(1+\theta)\phi^n-\theta \phi^{n-1}$ . The value of $\theta$ = thetvi is deduced from the value chosen for time_extrapolated key word for the viscosity. Generally, only the value 0.5 is used.

double precision, save	thetcp
	$\theta$ -scheme for the extrapolation of the physical property $\phi$ "specific heat" when the extrapolation has been activated (see time_extrapolated field key int), according to the formula $\phi^{n+\theta}=(1+\theta)\phi^n-\theta \phi^{n-1}$ . The value of $\theta$ = thetcp is deduced from the value chosen for the specific heat. Generally, only the value 0.5 is used.

double precision, dimension(nscamx), save	thetvs
	$\theta$ -scheme for the extrapolation of the physical property $\phi$ "diffusivity" when the extrapolation has been activated (see time_extrapolated key word), according to the formula $\phi^{n+\theta}=(1+\theta)\phi^n-\theta \phi^{n-1}$ . The value of $\theta$ = thetvs is deduced from the value chosen for time_extrapolated key word. Generally, only the value 0.5 is used.

real(c_double), pointer, save	epsup
	relative precision for the convergence test of the iterative process on pressure-velocity coupling (PISO)

real(c_double), pointer, save	xnrmu
	norm of the increment $\vect{u}^{k+1} - \vect{u}^k$ of the iterative process on pressure-velocity coupling (PISO)

real(c_double), pointer, save	xnrmu0
	norm of $\vect{u}^0$ (used by PISO algorithm)

Detailed Description

Variable Documentation

◆ epsup

real(c_double), pointer, save epsup

relative precision for the convergence test of the iterative process on pressure-velocity coupling (PISO)

◆ initcp

integer, save initcp

initcp : =1 if specific heat read from checkpoint file

◆ initro

integer, save initro

initro : =1 if density read from checkpoint file

◆ initvi

integer, save initvi

initvi : =1 if total viscosity read from checkpoint file

◆ initvs

integer, dimension(nscamx), save initvs

initvs : =1 if scalar diffusivity read from checkpoint file

◆ ischtp

integer, save ischtp

time order of time stepping

2: 2nd order
1: 1st order (default)

◆ isno2t

integer, save isno2t

isno2t specifies the time scheme activated for the source terms of the momentum equation, apart from convection and diffusion (for instance: head loss, transposed gradient, ...).

0: "standard" first-order: the terms which are linear functions of the solved variable are implicit and the others are explicit
1: second-order: the terms of the form $S_i\phi$ which are linear functions of the solved variable $\phi$ are expressed as second-order terms by interpolation (according to the formula $(S_i\phi)^{n+\theta}=S_i^n[(1-\theta)\phi^n+\theta\phi^{n+1}]$ , $\theta$ being given by the value of thetav associated with the variable $\phi$ ); the other terms are expressed as second-order terms by extrapolation (according to the formula $(S_e)^{n+\theta}=[(1+\theta)S_e^n-\theta S_e^{n-1}]$ , $\theta$ being given by the value of thetsn = 0.5).
2: the linear terms $S_i\phi$ are treated in the same way as when isno2t = 1; the other terms are extrapolated according to the same formula as when isno2t = 1, but with $\theta$ = thetsn = 1. By default, isno2t is initialised to 1 (second-order) when the selected time scheme is second-order (ischtp = 2), otherwise to 0.

◆ isso2t

integer, dimension(nscamx), save isso2t

for each scalar, isso2t specifies the time scheme activated for the source terms of the equation for the scalar, apart from convection and diffusion (for instance: variance production, user-specified terms, ...).

0: "standard" first-order: the terms which are linear functions of the solved variable are implicit and the others are explicit
1: second-order: the terms of the form $S_i\phi$ which are linear functions of the solved variable $\phi$ are expressed as second-order terms by interpolation (according to the formula $(S_i\phi)^{n+\theta}=S_i^n[(1-\theta)\phi^n+\theta\phi^{n+1}]$ , $\theta$ being given by the value of thetav associated with the variable $\phi$ ); the other terms are expressed as second-order terms by extrapolation (according to the formula $(S_e)^{n+\theta}=[(1+\theta)S_e^n-\theta S_e^{n-1}]$ , $\theta$ being given by the value of thetss (iscal) = 0.5)
2: the linear terms $S_i\phi$ are treated in the same way as when isso2t = 1; the other terms are extrapolated according to the same formula as when isso2t = 1, but with $\theta$ = thetss (iscal) = 1.
By default, isso2t (iscal) is initialised to 1 (second-order) when the selected time scheme is second-order (ischtp = 2), otherwise to 0.

◆ istmpf

integer, save istmpf

time order of the mass flux scheme The chosen value for istmpf will automatically determine the value given to the variable thetfl.

2: theta scheme with theta > 0 (theta=0.5 means 2nd order) the mass flow used in the momentum equations is extrapolated at n+ thetfl (= n+1/2) from the values at the two former time steps (Adams Bashforth); the mass flow used in the equations for turbulence and scalars is interpolated at time n+ thetfl (= n+1/2) from the values at the former time step and at the newly calculated time step.
0: theta scheme with theta = 0 (explicit): the mass flow calculated at the previous time step is used in the convective terms of all the equations (momentum, turbulence and scalars)
1: implicit scheme (default) : the mass flow calculated at the previous time step is used in the convective terms of the momentum equation, and the updated mass flow is used in the equations of turbulence and scalars. By default, istmpf=2 is used in the case of a second-order time scheme (if ischtp=2) and istmpf = 1 otherwise.

◆ isto2t

integer, save isto2t

isto2t specifies the time scheme activated for the source terms of the turbulence equations i.e. related to , $R_{ij}$ , $\varepsilon$ , $\omega$ , $\varphi$ , $\overline{f}$ ), apart from convection and diffusion.

0: standard first-order: the terms which are linear functions of the solved variable are implicit and the others are explicit
1: second-order: the terms of the form $S_i\phi$ which are linear functions of the solved variable $\phi$ are expressed as second-order terms by interpolation (according to the formula $(S_i\phi)^{n+\theta}=S_i^n[(1-\theta)\phi^n+\theta\phi^{n+1}]$ , $\theta$ being given by the value of thetav associated with the variable $\phi$ ); the other terms are expressed as second-order terms by extrapolation (according to the formula $(S_e)^{n+\theta}=[(1+\theta)S_e^n-\theta S_e^{n-1}]$ , $\theta$ being given by the value of thetst = 0.5)
2: the linear terms $S_i\phi$ are treated in the same way as when isto2t = 1; the other terms are extrapolated according to the same formula as when isto2t = 1, but with $\theta$ = thetst = 1.
Due to certain specific couplings between the turbulence equations, isto2t is allowed the value 1 or 2 only for the $R_{ij}$ models (iturb = 30 or 31); hence, it is always initialised to 0.

◆ nterup

integer(c_int), pointer, save nterup

number of interations on the pressure-velocity coupling on Navier-Stokes (for the PISO algorithm)

◆ thetcp

double precision, save thetcp

$\theta$ -scheme for the extrapolation of the physical property $\phi$ "specific heat" when the extrapolation has been activated (see time_extrapolated field key int), according to the formula $\phi^{n+\theta}=(1+\theta)\phi^n-\theta \phi^{n-1}$ .
The value of $\theta$ = thetcp is deduced from the value chosen for the specific heat. Generally, only the value 0.5 is used.

0 : explicit
1/2: extrapolated in n+1/2
1 : extrapolated in n+1

◆ thetfl

double precision, save thetfl

$\theta$ -scheme for the mass flux when a second-order time scheme has been activated for the mass flow (see istmpf).

0 : explicit first-order (corresponds to istmpf = 0 or 1)
1/2: extrapolated in n+1/2 (corresponds to istmpf = 2). The mass flux will be interpolated according to the formula $Q^{n+\theta}=\frac{1}{2-\theta}Q^{n+1}+\frac{1-\theta}{2-\theta}Q^{n+1-\theta}$ )
1 : extrapolated in n+1
Generally, only the value 0.5 is used.

◆ thetsn

double precision, save thetsn

$\theta_S$ -scheme for the source terms in the Navier-Stokes equations when the source term extrapolation has been activated (see isno2t), following the formula $(S_e)^{n+\theta}=(1+\theta)S_e^n-\theta S_e^{n-1}$ .
The value of = thetsn is deduced from the value chosen for isno2t. Generally only the value 0.5 is used.

0 : second viscosity explicit
1/2: second viscosity extrapolated in n+1/2
1 : second viscosity extrapolated in n+1

◆ thetss

double precision, dimension(nscamx), save thetss

$\theta$ -scheme for the extrapolation of the nonlinear explicit source term of the scalar transport equation when the source term extrapolation has been activated (see isso2t), following the formula $(S_e)^{n+\theta}=(1+\theta)S_e^n-\theta S_e^{n-1}$ .
The value of $\theta$ = thetss is deduced from the value chosen for isso2t. Generally, only the value 0.5 is used.

0 : explicit
1/2: extrapolated in n+1/2
1 : extrapolated in n+1

◆ thetst

double precision, save thetst

$\theta$ -scheme for the extrapolation of the nonlinear explicit source terms $S_e$ of the turbulence equations when the source term extrapolation has been activated (see isto2t), following the formula $(S_e)^{n+\theta}=(1+\theta)S_e^n-\theta S_e^{n-1}$ .
The value of is deduced from the value chosen for isto2t. Generally, only the value 0.5 is used.

0 : explicit
1/2: extrapolated in n+1/2
1 : extrapolated in n+1

◆ thetvi

double precision, save thetvi

$\theta$ -scheme for the extrapolation of the physical property $\phi$ "total viscosity" when the extrapolation has been activated (see time_extrapolated key word), according to the formula $\phi^{n+\theta}=(1+\theta)\phi^n-\theta \phi^{n-1}$ .
The value of $\theta$ = thetvi is deduced from the value chosen for time_extrapolated key word for the viscosity. Generally, only the value 0.5 is used.

0 : explicit
1/2: extrapolated in n+1/2
1 : extrapolated in n+1

◆ thetvs

double precision, dimension(nscamx), save thetvs

$\theta$ -scheme for the extrapolation of the physical property $\phi$ "diffusivity" when the extrapolation has been activated (see time_extrapolated key word), according to the formula $\phi^{n+\theta}=(1+\theta)\phi^n-\theta \phi^{n-1}$ .
The value of $\theta$ = thetvs is deduced from the value chosen for time_extrapolated key word. Generally, only the value 0.5 is used.

0 : explicit
1/2: extrapolated in n+1/2
1 : extrapolated in n+1

◆ xnrmu

real(c_double), pointer, save xnrmu

norm of the increment $\vect{u}^{k+1} - \vect{u}^k$ of the iterative process on pressure-velocity coupling (PISO)

◆ xnrmu0

real(c_double), pointer, save xnrmu0

norm of $\vect{u}^0$ (used by PISO algorithm)

Variables