OpenFOAM: перевод уравнений — различия между версиями

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+\frac{\partial W}{\partial z
 
+\frac{\partial W}{\partial z
 
}. </math>
 
}. </math>
 +
<math>
 +
\nabla \bullet T =
 +
\left(
 +
\begin{matrix}
 +
\frac{\partial }{\partial x_1}, & \frac{\partial }{\partial x_2}, & \frac{\partial}{\partial x_3}
 +
\end{matrix}
 +
\right)
 +
\bullet
 +
\left(
 +
\begin{matrix}
 +
T_{11} &    T_{12} &    T_{13}    \\
 +
T_{21} &    T_{22} &    T_{33}    \\
 +
T_{31} &    T_{32} &    T_{33}    \\
 +
\end{matrix}
 +
\right)
 +
=\partial_j T_{ji}=\left(
 +
\begin{matrix}
 +
\frac{\partial T_{11}}{\partial x_1}    + \frac{\partial T_{21}}{\partial x_2}    + \frac{\partial T_{31}}{\partial x_3}\\
 +
\frac{\partial T_{12}}{\partial x_1}    + \frac{\partial T_{22}}{\partial x_2}    + \frac{\partial T_{33}}{\partial x_3}\\
 +
\frac{\partial T_{13}}{\partial x_1}    + \frac{\partial T_{32}}{\partial x_2}    + \frac{\partial T_{33}}{\partial x_3}   
 +
\end{matrix}
 +
\right)
 +
</math>
 
|-
 
|-
 
| <math> \nabla \cdot \Gamma \nabla \psi </math> || fvm::laplacian(gamma, psi) ||
 
| <math> \nabla \cdot \Gamma \nabla \psi </math> || fvm::laplacian(gamma, psi) ||

Версия 22:56, 5 декабря 2015

Формула OpenFOAM Смысловое значение
$ \frac{\partial}{\partial t} \left(\rho \psi \right) $ fvm::ddt(rho, psi) Изменение величины во времени
$ \frac{\partial}{\partial t} \left(\rho \right) $ fvm::ddt(rho) Изменение величины во времени
$ \nabla \cdot \phi \psi $ fvm::div(phi, psi) $ \operatorname{div}\,\mathbf{F} = \nabla\cdot\mathbf{F} =\frac{\partial U}{\partial x} +\frac{\partial V}{\partial y} +\frac{\partial W}{\partial z }. $

$ \nabla \bullet T = \left( \begin{matrix} \frac{\partial }{\partial x_1}, & \frac{\partial }{\partial x_2}, & \frac{\partial}{\partial x_3} \end{matrix} \right) \bullet \left( \begin{matrix} T_{11} & T_{12} & T_{13} \\ T_{21} & T_{22} & T_{33} \\ T_{31} & T_{32} & T_{33} \\ \end{matrix} \right) =\partial_j T_{ji}=\left( \begin{matrix} \frac{\partial T_{11}}{\partial x_1} + \frac{\partial T_{21}}{\partial x_2} + \frac{\partial T_{31}}{\partial x_3}\\ \frac{\partial T_{12}}{\partial x_1} + \frac{\partial T_{22}}{\partial x_2} + \frac{\partial T_{33}}{\partial x_3}\\ \frac{\partial T_{13}}{\partial x_1} + \frac{\partial T_{32}}{\partial x_2} + \frac{\partial T_{33}}{\partial x_3} \end{matrix} \right) $

$ \nabla \cdot \Gamma \nabla \psi $ fvm::laplacian(gamma, psi)