做个笔记

[CFD中文网]

$$\begin{array}{}\text{(1)}& \frac{\mathrm{D}K}{\mathrm{D}t}=\frac{1}{2}\frac{\mathrm{D}|\mathbf{U}{|}^2}{\mathrm{D}t}=\frac{1}{2}\frac{\mathrm{D}{u}_i^2}{\mathrm{D}t}=\frac{1}{2}(\frac{\mathrm{\partial }{u}_i^2}{\mathrm{\partial }t}+\mathbf{U}\cdot \mathrm{\nabla }{u}_i^2)=u_i\frac{\mathrm{\partial }{u}_i}{\mathrm{\partial }t}+\mathbf{U}\cdot u_i\mathrm{\nabla }{u}_i=\frac{\mathrm{D}\mathbf{U}}{\mathrm{D}t}\cdot \mathbf{U}\end{array}$$

:sunglasses:

[CFD中文网]

$\mathrm{T}\mathrm{V}=\sum _i^{}|{\varphi }_{i+1}-{\varphi }_i|$