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For incompressible flow it has proven advantageous to use a second order scheme for all transient terms in the conservation equations. For instance, for the conservation of momentum equation this amounts to:
| \frac{\partial }{\partial t} \int_{V}^{} \rho v_i dv \approx \rho_P^{(m-1)} V_P \frac{ [3 v_i^{(m)}-4 v_i^{n-1}+ v_i^{n-2}] }{2 \Delta t}. | (759) |