Iform = 5
Block Format Keyword This boundary can simulate liquid inlet conditions for multimaterial ALE laws (formulation: I_{form} = 0, 1, 10, or 11).
The boundary submaterial state 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.
The user provides the stagnation where ${\alpha}_{stagnation}={\alpha}_{0}$ , ${\rho}_{stagnation}={\rho}_{0}$ , ${E}_{stagnation}={E}_{0}$ ( $E$ is optional) which corresponds to the state for which $\upsilon $ =0. From a linear EOS: ${P}_{0}={C}_{0}+{C}_{1}\mu $ ; thus ${P}_{stagnation}={C}_{0}$ .
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}  
${C}_{1}^{mat\text{\hspace{0.05em}}\_1}$  
$\Delta {P}_{min}^{\mathit{mat}\_1}$  ${C}_{0}^{mat\text{\hspace{0.05em}}\_1}$ 
(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}  
${C}_{1}^{mat\text{\hspace{0.05em}}\_2}$  
$\Delta {P}_{min}^{\mathit{mat}\_2}$  ${C}_{0}^{mat\text{\hspace{0.05em}}\_2}$ 
(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}  
${C}_{1}^{mat\text{\hspace{0.05em}}\_3}$  
$\Delta {P}_{min}^{\mathit{mat}\_3}$  ${C}_{0}^{mat\text{\hspace{0.05em}}\_3}$ 
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) 
$\left[\text{Pa}\right]$ 
${\alpha}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_\mathrm{i}}$  Initial volumetric fraction. 4 (Real) 

${\rho}_{0}^{\mathit{mat}\text{\hspace{0.05em}}\_\mathrm{i}}$  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
${\text{f}}_{{\alpha}_{i}}\left(t\right)$
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
${\text{f}}_{{E}_{i}}\left(t\right)$
identifier.
(Integer) 

${C}_{1}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}\mathrm{i}}$  Coefficient for perfect gas EOS. 5 (Real) 
$\left[\text{Pa}\right]$ 
$\Delta {P}_{min}^{\mathit{mat}\_i}$  Hydrodynamic cavitation pressure. 6 Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
${C}_{0}^{mat\text{\hspace{0.05em}}\_\text{}\text{\hspace{0.05em}}\mathrm{i}}$  Coefficient for perfect gas EOS. 5 (Real) 
$\left[\text{Pa}\right]$ 
Comments
 Provided gas state from stagnation point
${\rho}_{\mathit{stagnation}},\hspace{0.17em}{P}_{\mathit{stagnation}}$
is used to compute liquid inlet state. Bernoulli theory is
applied:
(1) $${P}_{\mathit{stagnation}}={P}_{\mathit{in}}+\frac{{\rho}_{\mathit{in}}{v}_{\mathit{in}}^{2}}{2}$$This leads to submaterial state in inlet boundary element:(2) $${\rho}_{in}=\frac{{C}_{1}\cdot {\rho}_{stagnation}}{{C}_{1}+\frac{{\rho}_{stagnation}{v}_{in}{}^{2}}{2}\left(1+{C}_{d}\right)}$$Where, ${C}_{d}$ is an optional drop parameter.(3) $${P}_{in}={P}_{stagnation}\frac{{\rho}_{stagnation}{v}_{in}{}^{2}}{2}\left(1+{C}_{d}\right)$$(4) $${\left(\rho e\right)}_{in}=\left(1\frac{{\rho}_{in}}{{\rho}_{stagnation}}\right){P}_{in}+{E}_{stagnation}$$Then global material state is determined by computing a mean value: Pressure
 $\Delta {P}_{in}=\sum _{i}{\alpha}^{ma{t}_{i}}(t)\Delta {P}_{in}^{mat\_i}$
 Density
 ${\rho}_{in}=\sum _{i}{\alpha}^{ma{t}_{i}}(t){\rho}_{in}^{mat\_i}$
 Energy
 ${(\rho e)}_{in}=\sum _{i}{\alpha}^{ma{t}_{i}}(t){\text{E}}_{in}^{mat\_i}$
 The optional scaling functions can be used such to scale the volumetric, density or energy fractions.
 Parameter P_{EXT} enables you to
take the 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.
Examples using linear EOS:
Total pressure: $P={P}_{amb}+{C}_{1}\mu $ , and also P_{EXT} = 0
Relative Pressure: $\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, ${\alpha}_{0}^{\mathit{mat}\_i}$ must be defined between 0 and 1.
Sum of initial volumetric fractions ${\sum}_{i=1}^{3}{\alpha}_{0}^{\mathit{mat}\_i}$ must be equal to 1.
For automatic initial fraction of the volume, refer to /INIVOL.
 Linear EOS is:
(5) $$P(\mu ,\hspace{0.17em}E)={C}_{0}+{C}_{1}\mu $$This provides flexibility, depending on whether pressure and energy are total or relative:(6) $$P(\mu ,\hspace{0.17em}E)={C}_{0}+{C}_{1}\mu $$Where, ${C}_{0}={P}_{\mathit{amp}},\hspace{0.17em}{C}_{1}={\rho}_{0}{c}_{0}^{2}$ and ${P}_{EXT}=0$ .
This leads to usual form from $P(\mu ,\hspace{0.17em}E)={C}_{0}+{C}_{1}\mu $ .(7) $$\Delta P(\mu ,\hspace{0.17em}E)={C}_{1}\mu $$Where ${C}_{1}={\rho}_{0}{c}_{0}^{2}$ and ${P}_{EXT}={P}_{amb}$ .

$\Delta {P}_{min}^{\mathit{mat}\_i}$
flag is the minimum value for the computed pressure.
Since $P=\text{\Delta}P+{P}_{EXT}$ , defining ${P}_{EXT}=0$ implies $\text{\Delta}P=P$ and $\text{\Delta}{P}_{\mathrm{min}}={P}_{\mathrm{min}}$ .
Fluid materials pressure must remain positive to avoid any tensile strength, then, ${P}_{min}=0$ leads to $\text{\Delta}{P}_{min}={P}_{EXT}$ .
For solid materials, the default value for $\Delta {P}_{min}^{\mathit{mat}\_i}$ = 10^{30} is suitable.
 Stagnation Energy is optional because this EOS does not depends on energy. The energy input value will only affect output value in animation files and time histories.
 EOS parameters must be consistent with liquid EOS from adjacent MMALE domain.