/MAT/LAW37 (BIPHAS)
Block Format Keyword Describes the hydrodynamic bimaterial liquid gas material. It is not recommended to use multimaterial laws with Radioss single precision engine.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW37/mat_ID/unit_ID or /MAT/BIPHAS/mat_ID/unit_ID  
mat_title  
P_{sh}  
${\rho}_{0}^{l}$  ${C}_{l}$  ${\alpha}_{l}$  ${\nu}_{l}$  ${\nu}_{vol\text{}\_\text{}l}$  
${\rho}_{0}^{g}$  $\gamma $  ${P}_{0}$  ${\nu}_{g}$  ${\nu}_{vol\text{}\_\text{}g}$ 
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) 

P_{sh}  Pressure
shift. 5 Default: ${P}_{sh}={P}_{0}$ (Real) 
$\left[\text{Pa}\right]$ 
${\rho}_{0}^{l}$  Liquid
reference density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
${C}_{l}$  Liquid bulk
modulus. (Real) 
$\left[\text{Pa}\right]$ 
${\alpha}_{l}$  Initial mass
fraction liquid proportion.
(Real) 

${\nu}_{l}$  Shear
kinematic viscosity (
$=\mu /{\rho}_{0}^{l}$
). (Real) 
$\left[\frac{{\text{m}}^{\text{2}}}{\text{s}}\right]$ 
${\nu}_{vol\text{}\_\text{}l}$  Volumetric
viscosity (kinematic) for liquid:
$=\frac{3\lambda +2\mu}{\rho}$
Default = 0: Stokes Hypothesis ( $3\lambda +2\mu =0$ ) (Real) 
$\left[\frac{{\text{m}}^{\text{2}}}{\text{s}}\right]$ 
${\rho}_{0}^{g}$  Reference
gas density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
$\gamma $  Perfect gas
constant. (Real) 

${P}_{0}$  Reference
gas initial pressure. (Real) 
$\left[\text{Pa}\right]$ 
${\nu}_{g}$  Shear
kinematic viscosity =
$=\mu /{\rho}_{0}^{g}$
. (Real) 
$\left[\frac{{\text{m}}^{\text{2}}}{\text{s}}\right]$ 
${\nu}_{vol\text{}\_\text{}g}$  Volumetric
viscosity (kinematic) for gas:
$=\frac{3\lambda +2\mu}{\rho}$
Default = 0: Stokes Hypothesis ( $3\lambda +2\mu =0$ ). (Real) 
$\left[\frac{{\text{m}}^{\text{2}}}{\text{s}}\right]$ 
Example
#RADIOSS STARTER
#12345678910
# 1. MATERIALS:
#12345678910
/UNIT/1
unit for mat
g mm ms
#12345678910
/MAT/LAW37/1/1
air (unit g_mm_ms)
# Psh
0
# RHO_l0 C_l ALPHA_l NU_l NU_VOL_l
.001 2089 0 1.787e3 0
# RHO_G0 GAMMA P0 NU_g NU_VOL_g
1.22E6 1.4 .1 1.48e2
/ALE/MAT/1
# Modif. factor.
0
/MAT/LAW37/2/1
water (unit g_mm_ms)
# Psh
0
# RHO_l0 C_l ALPHA_l NU_l NU_VOL_l
.001 2089 1 1.787e3 0
# RHO_G0 GAMMA P0 NU_g NU_VOL_g
1.22E6 1.4 .1 1.48e2
/ALE/MAT/2
# Modif. factor.
0
#12345678910
#enddata
#12345678910
Comments
 For each
cycle equilibrium is computed between liquid and gas:
$\mathrm{\text{\Delta}}{P}_{l}=\mathrm{\text{\Delta}}{P}_{g}$
Liquid EOS:
(1) $${P}_{l}={P}_{0}+{C}_{l}\mu $$with bulk modulus ${C}_{l}={\rho}_{0}^{l}{\left({c}_{0}^{l}\right)}^{2}$
Where, ${\rho}_{0}^{l}$
 Initial liquid density
 ${c}_{0}^{l}$
 Initial sound speed
Gas EOS:(2) $$P{v}^{\gamma}={P}_{0}{v}_{0}^{\gamma}=constant$$Where, P
 Pressure
 $v=\frac{V}{{V}_{0}}$
 Specific volume
Stress Tension(3) $$\sigma =P+\tau $$(4) $${\tau}_{ij}=\lambda {\dot{\epsilon}}_{kk}\text{\hspace{0.05em}}{\delta}_{ij}+2\mu {\dot{\epsilon}}_{ij}$$Where, $\sigma $
 Stress tension
 $P$
 Spherical stress tension
 $\tau $
 Viscous stress tension
 $\lambda $
 Shear viscosity (kinematic)
 $\mu $
 Dilatation viscosity (kinematic)
 Multimaterial LAW51 (/MAT/MULTIMAT) can emulate LAW37.
Antidiffusive technique using MUSCL method is under implementation. It is already available for LAW51 (/ALE/MUSCL).
 If inlet/outlet are needed LAW51 must be used instead. LAW51 has multi material inlet/outlet formulations.
 In Animation
files:
/ANIM/ELEM/DENS37 enables to output submaterial densities.
/ANIM/BRIC/VFRAC allows to output volumetric fractions for each submaterial.
Refer to Time Histories in the Radioss Starter Input Manual, or to /ANIM/Eltyp/Restype in the Radioss Engine Input Manual.
 By Default
${P}_{sh}={P}_{0}$
. This means that computed pressure is
shifted so that at initial time output pressure value relative to
${P}_{0}$
value is 0.0.To use total pressure, P_{sh} must be nullify using a small value such as 1e20 Pressure P could be exported in animation with /ANIM/ELEM/P.
Relative Pressure P_{sh}=P_{0} (Default)
Total Pressure P_{sh} = 1e20
Initial Condition: $P=\text{\Delta}P=0$ $P={P}_{0}$ Expansion: $P=\text{\Delta}P<0$ $P<{P}_{0}$ Compression: $P=\text{\Delta}P>0$ $P>{P}_{0}$  Internal Energy is not computed with LAW37. Nevertheless, adiabatic
condition
$dE=P\cdot dV$
is used through polytropic process
equation:
(5) $$P{V}^{\gamma}=const.$$  LAW37 is not compatible with elementary boundary conditions (/EBCS).