*UNDEX CHARGE PROPERTY

Data lines to define the UNDEX charge

First line

1. Charge material constant, K.

2. Charge material constant, k.

3. Charge material constant, A.

4. Charge material constant, B.

5. Adiabatic charge constant, $K_c$.

6. Ratio of specific heats for gas, $\gamma$.

Second line

1. Density of charge material, ${\rho }_c$.

2. Mass of charge material, $m_c$.

3. Acceleration due to gravity, g.

4. Atmospheric pressure, $p_{atm}$.

5. Wave effect parameter, $\eta$. Set to 1.0 for wave effects in the fluid and gas; set to 0.0 to neglect these effects. The default is 1.0.

6. Flow drag coefficient, $C_D$. The default is 0.0.

7. Flow drag exponent, $E_D$ ($E_D\ge 0$). The default is 2.0.

Third line

1. Time duration, $T_{\mathrm{final}}$.

2. Maximum number of time steps for the bubble simulation, $N_{\mathrm{steps}}$. The bubble amplitude simulation ceases when the number of steps reaches $N_{\mathrm{steps}}$ or the time duration, $T_{\mathrm{final}}$, is reached. The default is 1500.

3. Relative step size control parameter, ${\mathrm{\Omega }}_{\mathrm{rel}}$. The default is 1 × 10⁻¹¹.

4. Absolute step size control parameter, $X_{\mathrm{abs}}$. The default is 1 × 10⁻¹¹.

5. Step size control exponent, $\beta$. The step size, $\mathrm{\Delta }t$, is decreased or increased according to the error estimate: ${\left({\mathrm{\Omega }}_{\mathrm{rel}}\left|x\right|+X_{\mathrm{abs}}\right)}^{\beta }\le \mathrm{\Delta }t{\left|\frac{dx}{dt}\right|}^{\beta }$. The default is 0.2.

Fourth line

1. Depth magnitude of charge material, $d_I$.

2. X-direction cosine of fluid surface normal.

3. Y-direction cosine of fluid surface normal.

4. Z-direction cosine of fluid surface normal.