Ityp = 2
Block Format Keyword This law enables to model a material inlet/outlet by directly imposing its state. Input card is similar to /MAT/LAW11 (BOUND), but introduces two new lines to define turbulence parameters.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/BKEPS/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  ${\rho}_{0}$  
Ityp  P_{sh}  Fscale_{T} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

Blank Format  
fct_ID $\rho $  
fct_ID_{p}  P_{0}  
fct_ID_{E}  E_{0}  
${\rho}_{0}{\kappa}_{0}$  ${\rho}_{0}{\epsilon}_{0}$  fct_ID_{k}  fct_ID_{e}  
${C}_{\mu}$  ${\sigma}_{\kappa}$  ${\sigma}_{\epsilon}$  ${P}_{r}/{P}_{rt}$  
fct_ID_{T}  fct_ID_{Q} 
Definition
Field  Contents  SI Unit Example 

mat_ID  Material
identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

mat_title  Material
title. (Character, maximum 100 characters) 

${\rho}_{i}$  Initial density.
3 (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
${\rho}_{0}$  Reference density
used in E.O.S (equation of state). Default ${\rho}_{0}$ = ${\rho}_{i}$ (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
Ityp  Boundary condition
type. 1
(Integer) 

P_{sh}  Pressure shift.
3 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{T}  Time scale factor. 3 (Real) 

fct_ID $\rho $  Function
${\text{f}}_{\rho}\left(t\right)$
identifier for
boundary density. 3
(Integer) 

fct_ID_{p}  Function
${\text{f}}_{P}\left(t\right)$
identifier for
boundary pressure.. 3
(Integer) 

P_{0}  Initial pressure.
3 (Real) 
$\left[\text{Pa}\right]$ 
fct_ID_{E}  Function
${\text{f}}_{E}\left(t\right)$
identifier for boundary
energy. 3
(Integer) 

E_{0}  Initial energy.
3
6 (Real) 
$\left[\text{Pa}\right]$ 
${\rho}_{0}{\kappa}_{0}$  Initial turbulent
energy. (Real) 
$\left[\text{J}\right]$ 
${\rho}_{0}{\epsilon}_{0}$  Initial turbulent
dissipation. (Real) 
$\left[\text{J}\right]$ 
fct_ID_{k}  Function
${\text{f}}_{\kappa}\left(t\right)$
identifier for turbulence modeling.
(Integer) 

fct_ID_{ $\text{\epsilon}$ }  (Optional) Function
${\text{f}}_{\epsilon}\left(t\right)$
identifier for turbulence modeling.
(Integer) 

${C}_{\mu}$  Turbulent viscosity
coefficient. Default = 0.09 (Real) 

${\sigma}_{\kappa}$  Diffusion
coefficient for
$\kappa $
parameter. Default = 1.00 (Real) 

${\sigma}_{\epsilon}$  Diffusion
coefficient for
$\dot{\epsilon}$
parameter Default = 1.30 (Real) 

${P}_{r}/{P}_{rt}$  Ratio between
Laminar Prandtl number (Default 0.7) and turbulent Prandtl
number (Default 0.9). (Real) 

fct_ID_{T}  Function
${\text{f}}_{T}\left(t\right)$
identifier for inlet temperature.
(Integer) 

fct_ID_{Q}  Function
${\text{f}}_{Q}\left(t\right)$
identifier for inlet heat flux.
(Integer) 
Example (Gas)
#RADIOSS STARTER
#12345678910
/MAT/BKEPS/3
GAS INLET (unit: kg_m_s)
# RHO_I
.3828
# ITYP Psh Fscale_T
2
#blank line
# fct_RHO
1
# fct_P P_0
0
# fct_E E_0
1 253300
# Rho0k0 Rho0Eps0 fct_k fct_eps
20 0 1 0
# Cmu Sigmak Sigmaepsilon Pr/Prt
0 0 0 0
# fct_T fct_Q
/ALE/MAT/3
# Modif. factor.
0
#12345678910
/FUNCT/1
CST
# X Y
0 1
1.0E20 1
#12345678910
#enddata
/END
#12345678910
Comments
 Provided state is directly
imposed to inlet boundary elements. This leads to the following inlet state:$${\rho}_{in}={\rho}_{i}{\text{f}}_{\rho}\left(t\right)$$$${P}_{in}={P}_{0}{\text{f}}_{P}\left(t\right)$$$${E}_{in}={\left(\rho e\right)}_{in}={E}_{0}{\text{f}}_{E}\left(t\right)$$
With this formulation, you may impose velocity on boundary nodes to be consistent with physical inlet velocity (/IMPVEL). /MAT/LAW11  Ityp=0 and 1, are based on material state from stagnation point, where you do not need to imposed an inlet velocity.
 The P_{sh} parameter enables shifting the output pressure which also becomes PP_{sh}. If using ${P}_{sh}=P\left(t=0\right)$ , the output pressure will be $\text{\Delta}P$ , with an initial value of 0.0.
 If no function is defined, then related quantity ( ${P}_{stagnation},{\rho}_{stagnation},T$ , or Q) remains constant and set to its initial value. However, all input quantities ( ${P}_{stagnation},{\rho}_{stagnation},T$ , and Q) can be defined as time dependent function using provided function identifiers. Abscissa functions can also be scaled using Fscale_{T} parameter which leads to use $\mathrm{f}\left(Fscal{e}_{t},t\right)$ instead of $\mathrm{f}\left(t\right)$ .
 With thermal modeling, all thermal data ( ${T}_{0},{\rho}_{0}{C}_{p}$ , …) can be defined with /HEAT.
 It is not possible to use this boundary material law with multimaterial ALE /MAT/LAW37 (BIPHAS)) and /MAT/LAW51 (MULTIMAT).
 Specific volume energy
E is defined as
$E=\raisebox{1ex}{${E}_{\mathrm{int}}$}\!\left/ \!\raisebox{1ex}{$V$}\right.$
, Where
 ${E}_{int}$
 Internal energy. It can be output using /TH/BRIC.
Specific mass energy e is defined as $e={E}_{int}/m$ . This leads to $\rho e=E$ . Specific mass energy e can be output using /ANIM/ELEM/ENER. This may be a relative energy depending on user modeling.