Система уравнений скоростей и моментов сил

Last modified by Alexey Popov on 2019/09/24 14:22

${\frac {\partial {\vec {v}}}{\partial t}}=-({\vec {v}}\cdot \nabla ){\vec {v}}+\nu \Delta {\vec {v}} + \nabla \times \vec{m}+{\vec {a}},$

$\nabla \cdot {\vec {v}}=0$

${\frac{1}{c^2}\frac {\partial {\vec {m}}}{\partial t}}=-\frac{1}{c^2}({\vec {v}}\cdot \nabla ){\vec {m}}+ \frac{1}{c^2}\nu \Delta {\vec {m}} + \nabla \times \vec{v}-{\vec {\omega}},$

$\nabla \cdot {\vec {m}}=0$

$\nabla \cdot \vec{a} = \nabla \cdot ((\vec{v}\cdot \nabla )\vec{v}) = \frac{1}{2} \Delta (\vec{v}\cdot\vec{v}) - \nabla \cdot \left ( \vec{v} \times (\nabla \times \vec{v})\right )$

$\nabla \,\cdot \,\vec{\omega} = \frac{1}{c^2}\nabla \cdot ((\vec{v}\cdot \nabla )\vec{m}) = \frac{1}{2}\frac{1}{c^2} \left (\Delta (\vec{v}\cdot\vec{m}) - \vec{v}\cdot \Delta \vec{m} + \vec{m}\cdot \Delta \vec{v} \right ) \right ) -\frac{1}{c^2}\nabla \cdot \left (\vec{v} \times (\nabla \times \vec{m}))$

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Created by Alexey Popov on 2019/09/24 14:22