\[\frac{\partial }{\partialt}({{\varepsilon }_{g}}{{\rho }_{g}})+\nabla \cdot ({{\varepsilon }_{g}}{{\rho}_{g}}{{v}_{g}})={{S}_{g}}\]
\[\frac{\partial }{\partialt}({{\varepsilon }_{si}}{{\rho }_{si}})+\nabla \cdot ({{\varepsilon}_{si}}{{\rho }_{si}}{{v}_{si}})={{S}_{si}}\]