Iform = 6
Block Format Keyword This boundary material enables you to simulate a nonreflecting outlet boundary for multimaterial law /MAT/LAW51 (I_{form} = 0, 1, 10, or 11). This material is useful to model an infinite domain. Elements assigned this material law act like a nonreflecting elementary boundary.
This is an improvement of the formulation used with I_{form} = 3 and tends to minimize wave reflections and reverse flow problems. It includes both an acoustic treatment to avoid wave reflections on the outer limits of the computational domain and a “continuity” model for the volumetric fractions.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW51/mat_ID/unit_ID  
mat_title  
Blank Line  
I_{form}  
P_{ext}  T_{cp}  T_{ca} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\alpha}_{0}^{\mathit{mat}\_1}$  ${\rho}_{0}^{\mathit{mat}\_1}$  ${E}_{0}^{mat\_1}$  ${P}_{\mathrm{min}}^{mat\_1}$  ${P}_{0}^{mat\_1}$  
$ss{p}_{0}^{mat\_1}$  
Blank Line 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\alpha}_{0}^{\mathit{mat}\_2}$  ${\rho}_{0}^{\mathit{mat}\_2}$  ${E}_{0}^{mat\_2}$  ${P}_{\mathrm{min}}^{mat\_2}$  ${P}_{0}^{mat\_1}$  
$ss{p}_{0}^{mat\_2}$  
Blank Line 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\alpha}_{0}^{\mathit{mat}\_3}$  ${\rho}_{0}^{\mathit{mat}\_3}$  ${E}_{0}^{mat\_3}$  ${P}_{\mathrm{min}}^{mat\_3}$  ${P}_{0}^{mat\_1}$  
$ss{p}_{0}^{mat\_3}$  
Blank Line 
Definitions
Field  Contents  SI Unit Example 

mat_ID  Material identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Interger, maximum 10 digits) 

mat_title  Material title. (Character, maximum 100 characters) 

I_{form} 
(Integer) 

P_{ext}  External pressure . Default is computed by Starter (Real) 
$\left[\text{Pa}\right]$ 
T_{cp}  Characteristic time for pressure
relaxation. Default is computed by Starter (Real) 
$\left[\text{s}\right]$ 
T_{ca}  Characteristic time for volumetric
fraction relaxation . Default is computed by Starter (Real) 
$\left[\text{s}\right]$ 
${\alpha}_{0}^{\mathit{mat}\_j}$  Initial volumetric fraction for
submaterial #j=1...3. Default is computed by Starter (Real) 

${\rho}_{0}^{\mathit{mat}\_j}$  Initial density for submaterial
#j=1...3. Default is computed by Starter (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
${E}_{0}^{mat\_j}$  Initial volumetric energy for
submaterial #j=1...3. Default is computed by Starter (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
${P}_{\mathrm{min}}^{mat\_j}$  Pressure cutoff for submaterial
#j=1...3 . Default is computed by Starter (Real) 
$\left[\text{Pa}\right]$ 
${P}_{0}^{mat\_j}$  Initial pressure for submaterial #j=1..3
. Default is computed by Starter (Real) 
$\left[\text{Pa}\right]$ 
$ss{p}_{0}^{mat\_j}$  Initial sound speed for submaterial
#j=1..3 . Default is computed by Starter (Real) 
$\left[\frac{m}{s}\right]$ 
Example
#12345678910
/MAT/LAW51/1
Boundary Element, AUTOOUTLET
# IFORM
6
#Global parameters#
# PEXT TCP TC_ALPHA
0 0 0
#Material#1:#
# ALPHA_1 RHO_0_1 E_0_1 P_MIN_1 P_0_1
0 0 0 0 0
# SSP_1
0
#Material#2:#
# ALPHA_2 RHO_0_2 E_0_2 P_MIN_2 P_0_2
0 0 0 0 0
# SSP_2
0
#Material#3:#
# ALPHA_3 RHO_0_3 E_0_3 P_MIN_3 P_0_3
0 0 0 0 0
# SSP_3
0
#12345678910
Comments
 This pressure formulation is
derived from Bayliss and Turkel equations. 8
(1) $$\frac{\partial P}{\partial t}=\rho c\left(\frac{\partial {V}_{n}}{\partial t}{V}_{n}\cdot \mathrm{div}\left(V{V}_{n}n\right)\right)+\frac{c}{{T}_{cp}}\left({P}_{\infty}P\right)$$Where, $\rho c$
 Acoustic impedance
 ${P}_{\infty}$
 Far field pressure which is given as input unless the flux is coming inside the domain, i.e. normal velocity ${V}_{n}$ <0, where the stagnation pressure is imposed instead.
 Material advection is defined as:
 Outgoing flux: ${\alpha}_{i}={\alpha}_{i}^{neighbor}$
The local variable is simply updated. Incoming flux: $\frac{\delta {\alpha}_{i}}{\delta t}=\frac{\left{\alpha}_{i}^{0}{\alpha}_{i}\right}{{T}_{c\alpha}}$
The local variable is no longer updated as in the previous case, because this would assume that what happened inside the domain has also happened in the far field. It is however reasonable to consider that the material is locally similar to what it was before the flow was reversed. A relaxation factor is added, allowing the incoming materials to progressively return to the imposed value given in input.
 If not defined, the global parameter P_{ext} and the initial states are automatically computed from the adjacent elements.
 For the explosive submaterial, the initial state and data are always automatically computed using data from the adjacent elements.
 Each characteristic time can be calculated as the shortest time needed for the pressure wave (T_{cp}) or material (T_{ca}) to reach the closest limit of the domain as an order of magnitude. For incompressible cases, T_{cp} and T_{ca} can be taken as equal. For detonation or shock wave simulation, T_{cp} is calculated using an order of magnitude of the wave propagation velocity.
 It is advised that each outlet element share one face with one element from the ALE domain(s).
 The outlet boundary material is made of acoustic monopoles which imply that waves reaching the boundary should locally be approximated as plane waves or spherical waves. Therefore to correctly model the far field phenomena, the outlet elements should be located five to ten times the size of the explosive or impact area away from the explosive or impact area.
 Alvin Bayliss and Eli Turkel, Outflow boundary condition for fluid dynamics, Report 8021, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, Virginia