2.6.0.1 圧縮性流体（密度 [kg/m ]は変化する）

質量保存式

式(2.37) $^{\text{p.\pageref{eq-mass-com}}}$

$\displaystyle \frac{\partial \rho}{\partial t}$

$\displaystyle = - \bm{\nabla} \cdot ( \rho \bm{v})$

運動量保存式

式(2.90) $^{\text{p.\pageref{eq-momentum-com}}}$

$\displaystyle \frac{\partial \bm{v}}{\partial t}$	$\displaystyle = - \left( \begin{array}{c} \bm{v} \cdot \bm{\nabla} u \\ \bm{v} ... ...}(\bm{\nabla} \cdot \bm{v}) + \nu \bm{\nabla} \cdot \bm{\nabla} \bm{v} + \bm{g}$
$\displaystyle \left( \begin{array}{c} \dfrac{\partial u}{\partial t} \vspace{.5... ...\partial t} \vspace{.5em} \\ \dfrac{\partial w}{\partial t} \end{array} \right)$	$\displaystyle = \left( \begin{array}{c} - \bm{v} \cdot \bm{\nabla} u - \dfrac{1... ...t \bm{v} \big) + \bm{\nabla} \cdot \bm{\nabla} w \bigg\} \\ \end{array} \right)$

エネルギー保存式

式(2.187) $^{\text{p.\pageref{eq-energy-com}}}$

$\displaystyle \rho c_v \frac{\partial T}{\partial t} = - \rho c_v \bm{v} \cdot \bm{\nabla} T + k \bm{\nabla} \cdot \bm{\nabla} T - P \bm{\nabla} \cdot \bm{v}$