HD equations

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We try to write the formulas in its most general form and fix

First of all, in the simplest form of the HD equations we have

$latex frac{dboldsymbol{v}_a}{dt} = -sum_b m_b (frac{P_a}{rho_a^2} + frac{P_b}{rho_b^2}) nabla_a W_{ab}$ (momentum)

where:

$latex rho_a = sum_b m_b W_{ab}$ (density),

$latex frac{de_a}{dt} = frac{1}{2} sum_b m_b (frac{P_a}{rho_a^2} + frac{P_b}{rho_b^2}) boldsymbol{v}_{ab} cdot nabla_a W_{ab}$ (density energy),

$latex P_a$ and $latex P_b$

are obtained from the EoS and $latex frac{dboldsymbol{r}_a}{dt} = boldsymbol{v}_a$.

In SHD we have:

$latex d$

Finally, the GHD equations are:

$latex d$

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