Governing equations on differential form: Difference between revisions

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==== The Substantial Derivative ====
==== The Substantial Derivative ====


\noindent The substantial derivative operator is defined as\\
The substantial derivative operator is defined as


\begin{equation}
<math display="block">
\frac{D}{Dt}=\frac{\partial}{\partial t}+\mathbf{v}\cdot\nabla
\frac{D}{Dt}=\frac{\partial}{\partial t}+\mathbf{v}\cdot\nabla
\label{eq:substantial:derivative}
</math>
\end{equation}\\


\noindent where the first term of the right hand side is the local derivative and the second term is the convective derivative.\\
where the first term of the right hand side is the local derivative and the second term is the convective derivative.


==== Conservation of Mass ====
==== Conservation of Mass ====