Iform = 4
Block Format Keyword This boundary can simulate gas inlet conditions for multimaterial ALE laws (formulation: I_{form} = 0, 1, 10, or 11).
The boundary submaterial states is calculated from a state at a stagnation point which is provided by the user. When using this feature, it is no longer necessary to use imposed velocity (/IMPVEL) where the velocity is computed by numerical scheme.
Description
Where, ${C}_{4}=\gamma 1$ . It can be deduced that ${P}_{stagnation}={C}_{0}+{C}_{4}\cdot {E}_{0}$ .
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW51/mat_ID/unit_ID  
mat_title  
Blank Format  
I_{form} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

Scale_{time}  P_{EXT} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\alpha}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_1}$  ${\rho}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_1}$  ${E}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}1}$  fct_ID_{α1}  fct_ID_{ $\rho $ 1}  fct_ID_{E1}  
${C}_{1}^{mat\text{\hspace{0.05em}}\_1}$  ${C}_{4}^{mat\text{\hspace{0.05em}}\_1}$  
${C}_{0}^{mat\text{\hspace{0.05em}}\_1}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\alpha}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_2}$  ${\rho}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_2}$  ${E}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}2}$  fct_ID_{α2}  fct_ID_{ $\rho $ 2}  fct_ID_{E2}  
${C}_{1}^{mat\text{\hspace{0.05em}}\_2}$  ${C}_{4}^{mat\text{\hspace{0.05em}}\_2}$  
${C}_{0}^{mat\text{\hspace{0.05em}}\_2}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

${\alpha}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_3}$  ${\rho}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_3}$  ${E}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}3}$  fct_ID_{α3}  fct_ID_{ $\rho $ 3}  fct_ID_{E3}  
${C}_{1}^{mat\text{\hspace{0.05em}}\_3}$  ${C}_{4}^{mat\text{\hspace{0.05em}}\_3}$  
${C}_{0}^{mat\text{\hspace{0.05em}}\_3}$ 
Definition
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}  Formulation flag.
(Integer) 

Scale_{time}  Abscissa scale factor for input
functions. 2 Default = 1 (Real) 

P_{EXT}  External (ambient) pressure. 3 (Real) 
$\left[\text{Pa}\right]$ 
${\alpha}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_i}$  Initial volumetric fraction. 4 (Real) 

${\rho}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_i}$  Initial density at stagnation point.
1 (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
${E}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}\mathrm{i}}$  Initial energy at stagnation point.
5 (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
fct_ID_{αi}  (Optional)
Volumetric fraction scaling function.
${\mathrm{f}}_{{\alpha}_{i}}\left(t\right)$
identifier. 6
(Integer) 

fct_ID_{ $\rho $ i}  (Optional)
Density fraction scaling function.
${\text{f}}_{{\rho}_{i}}\left(t\right)$
identifier
(Integer) 

fct_ID_{Ei}  (Optional)
Energy fraction scaling function.
${\mathrm{f}}_{{E}_{i}}\left(t\right)$
identifier.
(Integer) 

${C}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}3}$  Coefficient for perfect gas EOS. 5 (Real) 
$\left[\text{Pa}\right]$ 
${C}_{4}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}\mathrm{i}}$  Perfect gas (
$\gamma 1$
) constant. 5 (Real) 

${C}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}\mathrm{i}}$  Coefficient for perfect gas EOS. 5 (Real) 
$\left[\text{Pa}\right]$ 
Comments
 The provided stagnation point
${\rho}_{\mathit{stagnation}},\hspace{0.17em}{P}_{\mathit{stagnation}}$
is used to compute gas inlet state. Bernoulli theorem is applied:
(2) $${P}_{\mathit{stagnation}}={P}_{\mathit{in}}+\frac{{\rho}_{\mathit{in}}{v}_{\mathit{in}}^{2}}{2}$$This leads to gas inlet state:(3) $${\rho}_{\mathit{in}}={\rho}_{\mathit{stagnation}}{[1\frac{\gamma 1}{2\gamma}\cdot \frac{{\rho}_{\mathit{stagnation}}}{{P}_{\mathit{stagnation}}}\cdot \left(1+{C}_{d}\right)\cdot {v}_{\mathit{in}}^{2}]}^{\frac{1}{\gamma 1}}$$(4) $${P}_{in}={P}_{stagnation}{\left(\frac{{\rho}_{in}}{{\rho}_{stagnation}}\right)}^{\gamma}$$(5) $${(\rho e)}_{in}=\frac{{P}_{a}}{\gamma 1}{\left(\frac{{\rho}_{in}}{{\rho}_{\mathit{stagnation}}}\right)}^{\gamma 1}$$Then the global material state is determined by computing a mean value: Pressure
 $\text{\Delta}{P}_{in}={\displaystyle {\sum}_{i}{\alpha}^{ma{t}_{i}}\left(t\right)\text{\Delta}{P}_{in}^{mat\_i}}$
 Density
 ${\rho}_{in}={\displaystyle {\sum}_{i}{\alpha}^{ma{t}_{i}}\left(t\right){\rho}_{in}^{mat\_i}}$
 Energy
 ${\left(\rho e\right)}_{in}={\displaystyle {\sum}_{i}{\alpha}^{ma{t}_{i}}\left(t\right){E}_{in}^{mat\_i}}$
 The optional scaling functions can be used such to scale the volumetric, density or energy fractions.
 Parameter
${P}_{EXT}$
enables you to take ambient pressure into account in case
you want to work with relative pressure
$\Delta {P}_{min}^{mat\_i}$
. This parameter is required by Radioss for correct energy integration at each cycle. Otherwise,
numerical EOS solving is generally incorrect. It represents pressure which must be added
to EOS calculation to obtain total (physical) pressure. It has no influence on pressure
contour in animation files.
Example using linear EOS:
Total Pressure: $P={P}_{\mathit{amb}}+{C}_{1}\mu $ and also ${P}_{EXT}=0$
Relative Pressure: $\text{\Delta}P={C}_{1}\mu $ , and also ${P}_{EXT}={P}_{amb}$
 Volumetric fractions enable the sharing of elementary volume within the three
different materials.
For each material, ${\alpha}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}i}$ must be defined between 0 and 1.
Sum of initial volumetric fractions $\sum}_{i=1}^{3}{\alpha}_{0}^{mat\text{}\_\text{}i$ must be equal to 1.
For automatic initial fraction of the volume, refer to /INIVOL.
 Perfect gas EOS is
$P\left(\mu ,E\right)=\left(\gamma 1\right)\left(1+\mu \right)$
. Generally it can be written using this general form
$P={C}_{0}+{C}_{1}\mu +{C}_{4}(1+\mu )E$
, where
${C}_{4}=\left(\gamma 1\right)$
. This provides more flexibility, depending on whether
pressure and energy are total or relative:
(6) $$P\left(\mu ,E\right)={C}_{4}\left(1+\mu \right)E$$Where, ${C}_{4}=\left(\gamma 1\right)$ and ${P}_{EXT}=0$ .
This leads to usual form from $\text{\Delta}P\left(\mu ,E\right)={C}_{0}+{C}_{4}\left(1+\mu \right)E$ .(7) $$\Delta P(\mu ,\hspace{0.17em}E)={C}_{0}+{C}_{4}(1+\mu )E$$Where, ${C}_{4}=\left(\gamma 1\right)$ , ${C}_{0}={P}_{0}$ and ${P}_{EXT}={P}_{amb}$ .(8) $$\text{\Delta}P\left(\mu ,\text{\Delta}E\right)={C}_{0}+{C}_{1}\mu +{C}_{4}\left(1+\mu \right)\text{\Delta}E$$Where, ${C}_{4}=\left(\gamma 1\right)$ , ${C}_{1}={E}_{0}\left(\gamma 1\right)$ and ${P}_{EXT}={P}_{amb}$ .

$\text{\Delta}{P}_{\mathrm{min}}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}i}$
flag is the minimum value for the computed pressure.
Since $P=\text{\Delta}P+{P}_{EXT}$ , defining ${P}_{EXT}=0$ implies $\text{\Delta}P\equiv P$ and $\text{\Delta}{P}_{min}\equiv {P}_{min}$ .
The materials pressure must remain positive to avoid any tensile strength, then, ${P}_{min}=0$ leads $\text{\Delta}{P}_{min}={P}_{EXT}$ .
For solid materials, the default value for $\text{\Delta}{P}_{\mathrm{min}}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}i}={10}^{30}$ is suitable.
 EOS parameters must be consistent with gas EOS from adjacent MMALE domain.