EOS_TILLOTSON
γSPH
Deprecated command
As a consequence of γSPH offboarding, this command will no longer work from June 1, 2025.
*EOS_TILLOTSON
eosid, $a$, $b$, $A$, $B$, $\alpha$, $\beta$, $e_0$
$e_{IV}$, $e_{CV}$, $\eta_{min}$, $\eta_{max}$, $p_{spall}$
eosid, $a$, $b$, $A$, $B$, $\alpha$, $\beta$, $e_0$
$e_{IV}$, $e_{CV}$, $\eta_{min}$, $\eta_{max}$, $p_{spall}$
Parameter definition
Variable
Description
eosid
Unique EOS identification number
$a$
Tillotson parameter
$b$
Tillotson parameter
$A$
Bulk modulus
$B$
Tillotson parameter
$\alpha$
Tillotson parameter
$\beta$
Tillotson parameter
$e_0$
Initial specific internal energy
$e_{IV}$
Incipient vaporization specific energy
$e_{CV}$
Complete vaporization specific energy
$\eta_{min}$
Compression threshold
$\eta_{max}$
Compression threshold
$p_{spall}$
Spall pressure
Description
This command is only supported by $\gamma SPH$.
State 1 - For compressed states where $\rho \geq \rho_0, e \geq 0$.
$\displaystyle{ p_1(\rho, e) = \left[ a - \frac{b}{\frac{e}{e_0 \eta^2} + 1} \right] \rho e + A \mu + B \mu^2 }$
where $\eta = \rho / \rho_0$ and $\mu = \eta - 1$.
State 2 - For cold expanded states where $\rho_0 \gt \rho, e \leq e_{IV}$.
$\displaystyle{ p_2(\rho, e) = \left[ a - \frac{b}{\frac{e}{e_0 \eta^2} + 1} \right] \rho e + A \mu + B \mu^2 }$
State 3 - For a mixed state $\rho_0 \gt \rho, e_{CV} \gt e \gt e_{IV}$.
$\displaystyle{ p_3(\rho, e) = \frac{(e - e_{IV}) p_4 + (e_{CV} - e) p_2}{e_{CV} - e} }$
State 4 - For hot expanded states where $\rho_0 \gt \rho, e \geq e_{CV}$.
$\displaystyle{ p_4(\rho, e) = a \rho e + \left[ \frac{b \rho e}{\frac{e}{e_0 \eta^2} + 1} + A \mu {\mathrm e}^{ -\beta \left( \frac{1}{\eta} - 1 \right) } \right] {\mathrm e}^{-\alpha \left( \frac{1}{\eta} - 1 \right)^2} }$
For condensed states (state $\leq 2$) and if $p \lt p_{spall}$, particle spalls and $p \lt 0$ is never allowed.
