Averaged Equations

Abstract

Averages of balance equations are obtained by taking the product of the balance equations with X _k , then performing the averaging process. We have:

$$\frac{{\overline {\partial {X_k}\rho \psi } }}{{\partial t}} + \nabla \cdot \overline {{X_k}\rho \psi v} - \nabla \cdot \overline {{X_k}J} - \overline {{X_k}\rho f} = \overline {\rho \psi (\frac{{\partial {X_k}}}{{\partial t}} + v \cdot \nabla {X_k})} - J \cdot \nabla {X_k}$$

(1)

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