非圧縮性一様流

\begin{eqnarray} && && &\frac{\partial }{\partial X_i} U_i& &=& 0 \\ && \frac{\partial }{\partial \tau} U_i &+& &\frac{\partial }{\partial X_j} U_j U_i& &=& -&\frac{\partial }{\partial X_i} P& + \frac{1}{Re} \frac{\partial^2 }{\partial X_j \partial X_j} U_i \\ \end{eqnarray}

上から連続の式、N-S方程式。以下無次元数

\begin{eqnarray} t &=& \frac{L}{U_a}\tau\\ u_i &=& U_a U_i \\ x_i &=& L X_i\\ p &=& p_0 + \rho_0 U_a^2 P\\ Re &=& \frac{L U_a}{\nu}\\ \end{eqnarray}