Ityp = 3
Block Format Keyword This law enables to model a nonreflecting boundary (NRF). 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} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

c  ${l}_{c}$  
Blank Format  
Blank Format  
Blank Format  
${\rho}_{0}{\kappa}_{0}$  ${\rho}_{0}{\epsilon}_{0}$  fct_ID_{k}  fct_ID_{e}  
${C}_{\mu}$  ${\sigma}_{\kappa}$  ${\sigma}_{\epsilon}$  ${P}_{r}/{P}_{rt}$  
Blank Format 
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. 2 (Real) 
$\left[\text{Pa}\right]$ 
c  Outlet sound speed. 1 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
${l}_{c}$  Characteristic length.
1 (Real) 
$\left[{\text{m}}^{3}\right]$ 
${\rho}_{0}{\kappa}_{0}$  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_{e}  Function f_{
$\text{\epsilon}$
}(t) identifier for energy.
(Integer) 

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

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

${\sigma}_{\epsilon}$  Diffusion coefficient for
$\text{\epsilon}$
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) 
Example (Gas)
#RADIOSS STARTER
#12345678910
/MAT/BKEPS/5
GAS OUTLET (unit: kg_m_s)
# RHO_I RHO_0
.3828 0
# ITYP Psh
3 0.0
# c lc
605 0.3
#blank line
#blank line
#blank line
# Rho0k0 Rho0Eps0 fct_k fct_eps
20 0 0 0
# Cmu Sigmak Sigmaepsilon Pr/Prt
0 0 0 0
#blank line
/ALE/MAT/5
# Modif. factor.
0
#12345678910
#enddata
/END
#12345678910
Comments
 NonReflecting Boundary
formulation is based on Bayliss & Turkel. ^{1} The objective is to impose a mean pressure
which fluctuate with rapid variations of pressure and velocity:
$\frac{\partial P}{\partial t}=\rho \text{\hspace{0.05em}}c\left(\frac{\partial}{\partial t}({V}_{n}){V}_{n}\cdot \mathrm{div}\left(V{V}_{n}\cdot n\right)\right)+c\frac{({P}_{\infty}P)}{2{l}_{c}}$
Pressure in the far field ${P}_{\infty}$ is imposed with a function of time. The transient pressure is derived from ${P}_{\infty}$ , the local velocity field V and the normal of the outlet facet: density, energy, temperature, turbulent energy and dissipation are imposed with a function of time as in Ityp = 2
 if the function number is 0, the neighbor element value is used to respect continuity
 acoustic impedance will be $\rho c$
 typical length
${l}_{c}$
is used to relax the effective
pressure towards its imposed value. It should be large compared to
the highest wave length of interest in the problem. The relaxation
term acts as high pass filter whose frequency cutoff
is:$${f}_{c}=\frac{c}{4\xb7\pi \xb7{l}_{c}}$$
Where, sound speed c and characteristic length ${l}_{c}$ are two required parameters (non zero).
 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.
 With thermal modeling, all thermal data ( ${T}_{0},{\rho}_{0}{C}_{p}$ , ...) can be defined with /HEAT/MAT.
 It is not possible to use this boundary material law with multimaterial ALE /MAT/LAW37 (BIPHAS) and /MAT/LAW51 (MULTIMAT).