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@东岳 谢谢！

尖的地方可以试试将多余的节点进行合并成一个节点映射到尖尖的点上，然后对锥块做一个Y剖，但是这样的话在尖尖位置的网格要么太密要么质量差

@东岳 感谢李老师！

I want to keep my bike close by, so I can fix it

I want to take off (remove) the bike wheel

Allen key

It doesn't fit

Move over, scoot over, can I get passed, please

She likes more and more like me everyday

I rarely (don't often) watch TV

Why did you set the temperature to 20 degrees

Dont rush me

I want to get rid of the extra oil

I can take some, I will finish what's left

She has a loose tooth, and its goin to fall out

She is not fully awake, she is a bit groggy

She is the one who loves me the most, she loves me the most

Put on the striped onesie

Move forwards and backwards

Her ton nail is broken

This is her first time seeing it

This drink is non-alcoholic, you can have a sip

Take a big step forward

A loose thread

Lift my leg and put it down

Stick out your tongue

She is lying on her side

I did it all in one go

Do you mind if I add her to our chat?

Please comment on the sentences above

Look at the lines on your arm. You leaned against something, that left lines on your arm.

Pull the handle to open the wardrobe

She just wants to be held up one your shoulder, she just wants to be held close to your chest

I am afraid of the dark

When she is sleeping, how does she know who is beside her

She does not care about anything, she is not easily bothered by things, she has high tolerance. I have a high pain tolerance.

If someone's ideas can be easily influenced by others,

She does not want to lean back

Give yourself a round of applause

Candy wrapper

I am meshing the pataya？？？

Are u scared of mosquitoes biting you?

Do you hear me calling you?

Another spoonful

How about I weigh you?

问题背景是在simpleFoam计算中添加被动标量运输，因此在controlDict里添加了function的scalarTransport。但是在设置参数的时候发现resetOnStartUp。
在源代码中的discription是Reset scalar to zero on start-up。
现在比较疑惑的是，如果打开resetOnStartUp:
１．是在每个时间增量计算开始时把标量reset为０
２．还是一整个计算结束后，再次重新计算时把标量设为０
大家有经验吗

\begin{equation}
\zeta =x-ct,\eta=x+ct
\end{equation}
\begin{equation}
\frac{\p\eta}{\p x}=1,\frac{\p\zeta}{\p x}=1
\end{equation}
\begin{equation}
\frac{\p\eta}{\p t}=c,\frac{\p\zeta}{\p t}=-c
\end{equation}
对任意变量关于$\zeta,\eta$的函数
\begin{equation}
\frac{\p}{\p x}=\frac{\p}{\p\eta}\frac{\p\eta}{\p x}+\frac{\p}{\p\zeta}\frac{\p\zeta}{\p x}=\frac{\p}{\p\eta}+\frac{\p}{\p\zeta}
\end{equation}
\begin{equation}
\frac{\p}{\p t}=\frac{\p}{\p\eta}\frac{\p\eta}{\p t}+\frac{\p}{\p\zeta}\frac{\p\zeta}{\p t}=c\frac{\p}{\p\eta}-c\frac{\p}{\p\zeta}
\end{equation}
\begin{equation}
\frac{\p^2}{\p x^2}=\left(\frac{\p}{\p\eta}+\frac{\p}{\p\zeta}\right)\left(\frac{\p}{\p\eta}+\frac{\p}{\p\zeta}\right)=\frac{\p^2}{\p\eta^2}+\frac{\p^2}{\p\zeta^2}+2\frac{\p^2}{\p\eta\p\zeta}
\end{equation}
\begin{equation}
\frac{\p^2}{\p t^2}=\left(c\frac{\p}{\p\eta}-c\frac{\p}{\p\zeta}\right)\left(c\frac{\p}{\p\eta}-c\frac{\p}{\p\zeta}\right)=c^2\frac{\p^2}{\p\eta^2}+c^2\frac{\p^2}{\p\zeta^2}-2c^2\frac{\p^2}{\p\eta\p\zeta}
\end{equation}

同理，下述网页中都需要处理$\sum_f p_f^{t}\bfS_f$为$\frac{1}{V_\rP}\sum_f p_f^{t}\bfS_f$，均已更正，谢谢

http://dyfluid.com/rhoPimpleFoam.html
http://dyfluid.com/rhoSimpleFoam.html
http://dyfluid.com/simplefoam.html

如题。

@akatsuki 是的，但是前面已经稳定了(后面其实也稳定了)，我是读取中间保存的cas和dat文件计算的

请教各位老师，外力驱动的流动，常用哪些算例做benchmark，比如Poiseuille流动，非定常的Womersley流动，还有吗？

速度的物质倒数两端乘以密度，再化简，就是时间项和对流项加在一起。

密度就是单位体积的质量，速度的物质导数就是加速度。
所以时间项和对流项加在一起就是单位体积内的$F=ma$，即$F=\rho a$。这就是惯性力吧？

力分为体积力和表面力，本来表面力应该是产生相对于体心的力矩。但是无限小体积的情况下把力臂忽略了（我猜的），力矩造成的转动靠物理规则演化出来而不故意设计出来。所以左边是流体微元变化需要的力，右边是流体微元真实受到的力，两者相等，就推出来流体微元怎么变化的了。

物理意义有助于了解方程怎么来的，但是后来方程形式因为代换化简早没有了当初的模样，只能从大概上理解。像广义的源项，这个和运输方程放在一起好理解。NS方程化简到最后是三个运输方程，运输的物理量分别是密度、速度、熵还是啥。源项，就像一个无源封闭体内进来多少就出去多少，但是有了源，就兴许进来的少出去的多。就是对运输产生了扰动。

要是搁到动量方程上，比如加个源项，磁流体在磁场中受电磁力，或者离心机里受额外的等效重力。

另外粘性造成的应力是和速度有关系的吧？叫本构关系，用来区别牛顿和非牛顿流体的。系数小不打紧，只要湍流涡够多，速度够快。耗散能量的能力就很强。

二变量高斯分布：
\begin{equation}
f(u,v)=\frac{1}{2\pi\sigma_1\sigma_2\sqrt{1-\rho^2}}\exp\left(-\frac{1}{2(1-\rho^2)}\left[\frac{(u-\mu_1)^2}{\sigma_1^2}-\frac{2\rho(u-\mu_1)(v-\mu_2)}{\sigma_1\sigma_2}+\frac{(v-\mu_2)^2}{\sigma_2^2}\right]\right)
\end{equation}
MGF为：
\begin{equation}
m_{i,j}=\exp\left(i\mu_1+j\mu_2+0.5(\sigma_1^2i^2+2\rho\sigma_1\sigma_2ij+\sigma_2^2j^2)\right)
\end{equation}
纯矩计算方法为
\begin{equation}
\begin{split}
m_{0,0}&=1\\
m_{1,0}&=\mu\\
m_{2,0}&=\mu^2+\sigma^2\\
m_{3,0}&=\mu^3+3\mu\sigma^2\\
\end{split}
\end{equation}
假设$\mu_1=10,\mu_2=20,\sigma_1=\sigma_2=2,\rho=0.5$，有纯矩：
\begin{split}
m_{0,0}&=1\\
m_{1,0}&=10\\
m_{2,0}&=104\\
m_{3,0}&=1120\\
m_{0,1}&=20\\
m_{0,2}&=404\\
m_{0,3}&=8240\\
\end{split}
同时有混合矩
\begin{equation}
m_{i,j}=\exp\left(36\right)
\end{equation}
不行，混合矩计算方法不对

不阔气不阔气，我也不是很懂，我猜的:chouchou:

@东岳 。。。多谢解答

是OpenFOAM吗？
如果是的话参考
https://www.cfd-online.com/Forums/openfoam-meshing/61596-cyclic-bcs-pointwiseopenfoam-export.html

@东岳 @Hunahum ，我在cfd-online上看到这样一段代码，想尝试着写出来，不过总是报错，请问你知道问题在哪儿吗1.png 2.png 3.png

@两月三年 good ，好主意。我试试哈。

pEqn里面用到了rAUc

@bestucan 好的，多谢