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23.3.4 Momentum Equation

A single momentum equation is solved throughout the domain, and the resulting velocity field is shared among the phases. The momentum equation, shown below, is dependent on the volume fractions of all phases through the properties $\rho$ and $\mu$.

 \frac{\partial}{\partial t} (\rho {\vec v}) + \nabla \cdot... ...bla {\vec v} ^{\rm T}\right)\right] + \rho {\vec g} + {\vec F} (23.3-7)

One limitation of the shared-fields approximation is that in cases where large velocity differences exist between the phases, the accuracy of the velocities computed near the interface can be adversely affected.

Note that if the viscosity ratio is more than $1 x 10^3$, this may lead to convergence difficulties. The compressive interface capturing scheme for arbitrary meshes (CICSAM) (Section  23.3.2) is suitable for flows with high ratios of viscosities between the phases, thus solving the problem of poor convergence.

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