/EOS/LINEAR

Block Format Keyword Describes the linear equation of state $P\left(\mu \right)={P}_{0}+B\mu$ with initial pressure and bulk modulus.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/LINEAR/mat_ID/unit_ID
eos_title
${P}_{0}$ B Psh

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID Unit Identifier.

(Integer, maximum 10 digits)

eos_title EOS title.

(Character, maximum 100 characters)

${P}_{0}$ Initial pressure.

(Real)

$\left[\text{Pa}\right]$
B Bulk modulus.

(Real)

$\left[\text{Pa}\right]$
Psh Pressure shift.

(Real)

$\left[\text{Pa}\right]$

Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW06/7/1
fluid material
#              RHO_I
0.001
#                 NU                PMIN
0               1e-20
/EOS/LINEAR/7/1
Water (linear approximation, Bulk = rho.c^2 = 0.001*1500*1500)
#                 P0                   B                 PSH
0.1              2250.0                 0.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

1. Linear EOS has the following form:
$P\left(\mu \right)={P}_{0}+B\mu$

Where,

$µ=\frac{\rho }{{\rho }_{0}}-1$

which can be derived from a polynomial EOS:

$P={C}_{0}+{C}_{1}\mu +{C}_{2}{\mu }^{2}+{C}_{3}{\mu }^{3}+\left({C}_{4}+{C}_{5}\mu \right){E}_{0}$

Where,
${C}_{0}={P}_{0}$
${C}_{1}=B$
${C}_{2}={C}_{3}={C}_{4}={C}_{5}=0$
2. Bulk modulus is usually estimated as:
$B={\rho }_{0}\cdot {c}_{0}{}^{2}$

Where, ${c}_{0}$ is the initial sound speed.

3. Psh parameter enables to shift output pressure. Output pressure will also be a relative pressure $\text{Δ}P\left(\mu \right)=P-{P}_{sh}$ .
4. Equations of state are used by Radioss to compute the hydrodynamic pressure and are compatible with the material laws:
• /MAT/LAW3 (HYDPLA)
• /MAT/LAW4 (HYD_JCOOK)
• /MAT/LAW6 (HYDRO or HYD_VISC)
• /MAT/LAW10 (DPRAG1)
• /MAT/LAW12 (3D_COMP)
• /MAT/LAW49 (STEINB)
• /MAT/LAW102 (DPRAG2)
• /MAT/LAW103 (HENSEL-SPITTEL)
• /MAT/LAW109