Topics created by 李东岳

https://www.cfd-china.com/topic/5198

参考这个帖子，有人可以做个STAR-CCM、COMSOL、CFX的算例么？

@李东岳 噢噢，好的

部分邮件我这面没法回复，因为每天都有几十封进来处理，下面是某一天下午5点多到晚上的，就这么多。

捕获.PNG

建筑环境湍流那边很多人都这么算的，比如

Anderson W. Amplitude modulation of streamwise velocity fluctuations in the roughness sublayer: evidence from large-eddy simulations[J]. Journal of Fluid Mechanics, 2016, 789: 567-588.

已经收到了

http://www.dyfluid.cn/theory.pdf

合适的内容我会更新在《无痛苦NS方程笔记》里面。

mark 一下

好像我问的有问题，$A=0.5(\overline{p_1}-\overline{p_0})\times(\overline{p_2}-\overline{p_0})$这个东西看起来是个矢量。但是面积不是矢量啊。我回去对对OpenFOAM的代码。

我看了下，OpenFOAM里面mesh.Sf()对应的是这个：$0.5(\overline{p_1}-\overline{p_0})\times(\overline{p_2}-\overline{p_0})$，mesh.magSf()对应的是这个：$\left|0.5(\overline{p_1}-\overline{p_0})\times(\overline{p_2}-\overline{p_0})\right|$，后面这个应该就是面积了。

@evensun $\left|0.5(\overline{p_1}-\overline{p_0})\times(\overline{p_2}-\overline{p_0})\right|$ 这个面积可以理解不

论坛每天都有3 4万点击，一万多IP，也不知道啥时候处理好 :143:

不知道他们几千万的CFD算法研究经费都是怎么构成的 :143:

@同学博 :jingya: 那我还不太知道。不知道这俩是不是一个东西。激光电视目前倒是销量比较差 :qichuang:

@马乔 :chouchou:

东岳老师这里有别人测试的结果吗，想对比一下:xiexie:

2021-09-17 15-46-22屏幕截图.png

背景：我要做自己的CFD软件，有生之年，跟商软来一次硬刚！

我这面目前要做的东西是基于OpenFOAM的CFD软件。OpenFOAM是一个国外的开源的CFD求解器，类似linux内核或安卓。我这面就是要基于国外的OpenFOAM内核，做一个中文的界面出来。就类似小米的MIUI手机系统。软件做出来之后就是国产CFD软件。但是内核是基于OpenFOAM。具体为什么要基于OpenFOAM而不是自己写。主要有2个原因：1）自己写出来的CFD代码没人信，2）所需要的时间要三五倍以上。这也就类似目前的C++，C++是国外提出来的，目前大可以放心使用，没必要自己从头开发一个编程语言。

在有了高度开发化的CFD求解器核心之后，在顶层GUI设计的过程中，要充分的做一个新东西出来：1）不能基于老套路。要按照CFD用户最方便的角度去重新设计。2）要把CFD相关的经验融合进去。做智能化，最易用的操作。目前的CFD软件还不够智能，比如商软，她会给你提供一系列的湍流模型可以选择，但是不会给你提供一个最优解。那这个CFD软件在做的时候，要克服相关的缺点。

软件做出来之后，基于我对产品的前沿性的设计。我有充分的信心和十足的把握去推动。软件要按照GPL协议，必然是要提供免费试用版。但同时，可以提供定制版，这部分可以获取利润。目前国内CFD软件的打法，都是直接推收费版软件。我觉得在没有人用的前提下，这些软件是推不出去的。可以赚些小钱，但是不会做成一个国家层面的具有影响力的工业软件。

我对这个产品具有充分的信心把它推出去。到时候只要国人用CFD，那除了商软，开源openfoam，我希望大家能想起这个。这么多年来国家一直在推国产工业软件，我国确实也有，但是没有一个让大家能说得出手。我国有些软件做的不错了，比如金山软件可以抗衡office，中望CAD可以抗衡SolidWorks。但CFD领域却没有人能说我国的xxx能与国外抗衡。我要做的，就是在这个空白的地方做出一个产品。这个软件对标的市场就是西方国家在国内售卖的CFD商业软件。

对合作方要说的：

要充分理解我做CFD软件的目的。我要做出一个最适合国内工业界的普适性CFD软件。希望真正的能让大家用起来。这建立在软件充分的“好用”的基础上。用户占有率在第一位。 也希望能认识到，免费产品未必不可盈利。如微信、抖音、快手、QQ、淘宝等。另一方面。工业软件投入的周期非常长，资本可以做一定程度的催化剂，但底层算法开发以及软件的更新迭代需要长期的坚守。

捐赠

我个人认为这个事情很难做成。主要就是缺少一个前端，普通前端的工资不低，一年30万打底。好一点的一年得更多。咱也没有这个钱一直去投入。目前尚且没有国家基金以及民间资本对这个项目进行支持。于是我决定尝试最后一条路，虽然希望也很渺茫，那就是捐赠。

我个人的想法是在最短的时间内，募集最少40万元，来支付一个前端的工资。当然在法律层面可能需要斟酌（比如一年期聘用关系？）同时，为了保证资金的透明。我这面可以做以下承诺：

2024年9月1日，捐赠达到40万元，我自己将出10万元，凑够50万元，用于第一年的业务支出（40万元用于发工资，10万元用于成立公司组办公室等杂项）。同时继续募集资金用于下一年的支出。

2024年9月1日，不足40万元。项目终止。资金退回给捐赠者。

如果在此期间中彩票拿到天使投，资金退回给捐赠者。

如果在此期间有合作方可以投人，那表明不需要额外资金招聘，资金退回给捐赠者。

捐赠期间，款项进出都将在本帖公示。

捐赠方式

如果是一些个人的捐赠，请参考下方的微信支付二维码。

如果是一些机构的捐赠。可以通过合作的方式来进行。例如，我这面有服务器售价5万元，合作方若愿意捐赠1万元，可走6万元的合同。其中差价1万元则进入本项目捐赠资金。其他的与我这面的其他项目合作都可以，如CFD项目、CFD课程之类。

也希望大家多多宣传。CFD这面我可以弄，最需要的就是一个能做事情的前端。谢谢大家。:xiexie:

资金列表 日期 机构/个人/匿名 金额 备注

@李东岳 铁人都不睡觉的:136:

@袁宝强 啊我知道了 谢谢 :xiexie:

@liujiaming
您是刘超群老师课题组访学的那位刘剑明老师吗？久仰久仰

变成了这样：transformPoints 'scale=(0.01 0.01 0.01)'

之前是这样：transformPoints -scale ‘(0.01 0.01 0.01)'

https://github.com/OpenFOAM/OpenFOAM-dev/commit/845d5b16e30d568af3eb71c69ff7f8079347522e

paraFoam -builtin也可以

前几天OpenFOAM基金会在群里面发了个消息，说OpenFOAM-9发布啦！然后一片死寂，一个人都没有，跟咱们中国的夸夸群差远了，于是基金会补上了一张图，就是这面这个

tumbleweed.gif

给我笑爆了..

@李东岳 果然有了，谢谢老师

@李东岳 东岳老师，这个就已经够用了:huahua:

@星星星星晴 我赶紧摸一下木头！

我们家小盆友找的加拿大小姐姐从学校（人民大学）里面出不来了..

2021-08-08 20-06-30屏幕截图.png

@李东岳 李老师有没有兴趣看下风工程这块的有个商业软件WT，里面是速度-压力耦合求解器，真的非常快非常快。我看了下，软件底层是从PHOENICS来的，然后搞了一套叫MIGAL的算法。

现在CFD用的SIMPLE这种segregated solver确实太慢了，城市这种尺度下的流动本身大概率又比较简单，不可压，也没有化学反应之类的，可以暂时不考虑温度？可能会有颗粒流的问题，但是不是也可以先只考虑流动对颗粒的影响。这种情况下感觉流场本身的求解其实就看求解器的效率了。

我搜了下，OpenFOAM这边其实已经有一些coupled solver 的工作，不知道成不成熟。

@gemini 比较细的粉尘 地面一层灰那种情况 :huahua:

ffmpeg -i input.MP4 -c:v libx264 -preset slow -crf 40 -c:a copy output.mp4

https://stackoverflow.com/questions/30304794/gnuplot-command-with-multiple-with-arguments

@李东岳 谢谢东岳教授

对于给定的NDF，划分为$i$个$N_{pp}$，对每个$i$上定义$k$阶矩$m_k^i$，给定$m_k^i$，可以计算第$i$区间的节点$d^i_0,d^i_1$以及权重$w^i_0,w^i_1$：
\begin{equation}
\begin{split}
w^i_0&=w^i_1=0.5
\\
d^i_0&=m_1^i-\frac{1}{\sqrt{3}}\sqrt{\frac{m_3^i}{m_1^i}-{m_1^i}^2}
\\
d^i_1&=m_1^i+\frac{1}{\sqrt{3}}\sqrt{\frac{m_3^i}{m_1^i}-{m_1^i}^2}
\end{split}
\end{equation}
对于仅考虑破碎的PBE：
\begin{equation}\label{pbe}
\frac{\p n(d)}{\p t}=\int_d^{d_{max}}g(d')\beta(d|d')n(d')\rd d'-g(d)n(d)
\end{equation}
对方程\eqref{pbe}在$i$上取$k$阶矩：
\begin{equation}\label{m}
\frac{\p m_k^i}{\p t}=\int_{d_{i-1/2}}^{d_{i+1/2}}\int_d^{d_{max}}g(d')d^k\beta(d|d')n(d')\rd d'\rd d-\sum^2_{j=0} g(d_j^i)w_j^i(d_j^i)^k
\end{equation}
\begin{equation}
\begin{split}
\int_{d_{i-1/2}}^{d_{i+1/2}}\int_d^{d_{max}}g(d')\beta(d|d')n(d')\rd d'\rd d&=
\int_{d_{i-1/2}}^{d_{max}}g(d')n(d')\left(\int_{d_{i-1/2}}^{d'}\beta(d|d')\rd d\right)\rd d'
\\&=
\sum_{m=i}^{N}\sum_{j=0}^2g(d_j^m)w_j^m\left(\int_{d_{i-1/2}}^{d_j^m}d^k\beta(d|d_j^m)\rd d\right)
\end{split}
\end{equation}
Therefore
\begin{equation}
\frac{\p m_k^i}{\p t}=\sum_{m=i}^{N}\sum_{j=0}^2g(d_j^m)w_j^m\left(\int_{d_{i-1/2}}^{d_j^m}d^k\beta(d|d_j^m)\rd d\right)-\sum^2_{j=0} g(d_j^i)w_j^i(d_j^i)^k
\end{equation}

The objective of this link is to provide a resource for CFD developers to:

obtain different gas-liquid benchmark test cases for validation and verification, verify related CFD models are implemented correctly.

This latter capability is made possible through benchmark cases. This site provides simple test cases and grids, along with sample results from experiments which are mainly reported in previous published works. All the test cases are prepared as standard cases for open-source code OpenFOAM-8. It can be run by the following command in the terminal:./Allrun

The site should also help CFD code users to understand and compare the predictions of a variety of models on the fundamental flow problems in the validation database. It also helps developers to disseminate new models to the CFD community.

It is anticipated that this word will be updated regularly as new models and/or verification/validation cases are incorporated and tested. If you have any questions or comments, please contact one of the authors: Dongyue Li (li.dy@dyfluid.com)

1. Diaz et al. 2008

Features: This test case is a laboratory rectangle turbulent bubble column. The gas was injected in the middle of the bottom, which implies the geometry is quite symmetric. Nonetheless, it was also shown that the dynamic periodic liquid circulation can be founded in experiments. Simulations should be able to predict such periodic bubble plume with only the drag model. In addition, the authors also investigated the role of lift force and virtual mass force. The geometry is simple and settings are clear. This test case is suitable for investigate numerical algorithm. It should be noted here that the mean Sauter diameter data was also provided, although not in detail.

Keywords: Unsteady, Rectangle bubble column, Mean Sauter diameter, Bubble plume,

Reference: Díaz et al. "Numerical simulation of the gas–liquid flow in a laboratory scale bubble column: influence of bubble size distribution and non-drag forces." Chemical Engineering Journal 139.2 (2008): 363-379.

bubbleFlow_diaz.jpg

2. Gemello et al. 2018

Features: This test case focuses on the unsteady 3D bubble column operated under high phase fration. Different swarm models were studied and a new swarm model was developed. The diameter of the bubble column ranges from 0.4m to 1m. Different superficial velocities from 0.03 m/s to 0.35 m/s were employed. This test case is suitable for investigate the swarm model correction based on different operating conditions.

Keywords: Unsteady, 3D bubble column, Swarm effect, High phase fraction,

Reference: Gemello et al. "CFD-based scale-up of hydrodynamics and mixing in bubble columns." Chemical Engineering Research and Design 136 (2018): 846-858.

bubbleFlow_Gemello.jpg

3. Lucas et al. 2007

Features: In the work of Lucas et al., bubbly flow in a high aspect ratio column (Column width ~ 0.05 m, Column height ~ 4 m) was investigated. Bubbles and liquid are injected from the bottom. They move upward and at a certain level a fully developed flow pattern is formed. In both experiments and simulations, a quite steady state can be reached at the top of the column. These bubbly flows are operated at relative low phase fraction (~ 3%). The most important feature of the test cases by Lucas et al. is that the momentum exchange interfacial terms play an important role. It was observed in the experiments that the small bubbles tend to move towards to wall. Therefore, a wall peak of the phase fraction should be predicted in simulations. It should be noted here that the lift force, wall lubrication force and turbulent dispersion force should be included.

Keywords: Steady, Bubbly flow, Lift force, Wall forces

Reference: Lucas et al., "Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows." Chemical Engineering Science 62.15 (2007): 4146-4157.

bubbleFlow_Lucas.jpg

4. Yuan et al. 2014

Features: In the work of Yuan et al., an experimantal quasi-2D bubble column was investigated. In the simulations, 2D computational domain was employed. The bubbles are injected from the bottom of the column with different patterns. Overall 5 patterns were studied. Due to the high superficial velocity, simulations are highly transient. In this work, the QBMM was used to predict bubble diameter. However, the experimental diameter data was not reported. The bubble number density function was also reconstructed by EQMOM. It should be noted here that the experimental data reported in Yuan et al. comes from the PhD thesis of Harteveld, see ref (8) in Yuan et al.

Keywords: Unsteady, Bubble column, 2D simulation

Reference: Yuan et al., "An extended quadrature‐based mass‐velocity moment model for polydisperse bubbly flows." The Canadian Journal of Chemical Engineering 92.12 (2014): 2053-2066.

bubbleFlow_Yuan.jpg

5. Schafer et al. 2019

Features: In the work of Schafer et al., a 3D transient bubble column was studied by experiments and simulations. The geometry used in this work is similar with that used by Diaz et al. The unique feature of this work is that the bubble orientation angle data was provided. It can be used as a benchmark test case for multiphase DNS. Besides that, the bubble diameter NDF was also provided both in experiments and simulations. The so-called SQMOM, as a kind of QBMM, was used predict the bubble NDF at different locations and it was compared with experiments.

Keywords: Unsteady, 3D simulation, NDF reconstruction, SQMOM, Bubble orientation angle

Reference: Schäfer et al., "Experimental investigation of local bubble properties: Comparison to the sectional quadrature method of moments." AIChE Journal 65.10 (2019): e16694.

bubbleFlow_Schafer.jpg

6. Li et al. 2021

Features: In the work of Li et al., three 3D transient bubble column was studied to verify the algorithm. One of test case was reported in Diaz et al. The other one consists of a similar partially aerated rectangle bubble column which was investigated experimentally by Becker et al. in 1994. The left one is an airlift bubble column investigated by Mandalahalli et al. Li et al. developed a new algorithm which is much faster than the traditional Eulerian-Eulerian method and used it to simulate three different bubbly flows as mentioned above. Only drag force needs to be included (the last airlift bubble column also needs the turbulent dispersion force). These test cases are suitable to validate new developed algorithms.

Keywords: Unsteady, 3D simulation, Airlift bubble column, Particlly aerated

Reference: Li et al. "QEEFoam: A Quasi-Eulerian-Eulerian model for polydisperse turbulent gas-liquid flows. Implementation in OpenFOAM, verification and validation." International Journal of Multiphase Flow 136 (2021): 103544.

bubbleFlow_Li.jpg

7. Besbes et al. 2015

Features: In the work of Besbes et al., a needle sparger rectangular bubble column operated at low flow rates was investigated using PIV measurements and Eulerian-Lagrangian simulations. Time-averaged liquid velocity fields from PIV measurements for different flow rate were provided. Snapshots of PIV and Eulerian-Lagrangian simulation of oscillating bubble plume were also supplied. Due to the small flow rate and the usage of a needle sparger, the diameter of bubbles is very homogeneous. The oscillatory movement of bubble plume, as that observed in Diaz et al., was also formed for slightly large flow rate (Q = 0.2 l/min).

Keywords: Needle sparger, Eulerian-Largrangian, PIV

Reference: Besbes et al., "PIV measurements and Eulerian–Lagrangian simulations of the unsteady gas–liquid flow in a needle sparger rectangular bubble column." Chemical Engineering Science 126 (2015): 560-572.

bubbleFlow_Besbes.jpg

8. Darmana et al. 2007

Features: In this work, a rectangle laboratory bubble column was used to study the bubble flow with reactions. A pseudo-2D geometry is chosen to enable visualization of the flow structures by CCD camera and PIV. Lagrangian simulations were also launched. Averaged velocities, bubble plume period, gas holdup and global mean Sauter diameter were also compared with experiments. The species's concentration and Ph value were also provided.

Keywords: Reaction bubble column, Mass transfer, mean Sauter diameter

Reference: Darmana et al. "Detailed modelling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model: Chemisorption of CO2 into NaOH solution, numerical and experimental study." Chemical Engineering Science 62.9 (2007): 2556-2575.

bubbleFlow_Darmana.jpg

9. Besbes et al. 2020

Features: In this work, the authors employ PIV technique to study the liquid phase flow driven by a chain of air bubbles in a rectangular bubble column. The flow rate is very low that each bubble move upward separately by buoyancy force. Not only water, but also the glycerin solution with high viscosity was studied to understand the liquid flow structure. Bubble terminal velocity and shape were also provided.

Keywords: PIV, Bubble driven flow, High viscosity

Reference: Besbes et al., "Effect of bubble plume on liquid phase flow structures using PIV." Particulate Science and Technology 38.8 (2020): 963-972.

bubbleFlow_Besbes2.jpg

Test Case Diaz et al. 2004 Gemello et al. 2018 Yuan et al. 2014 Lucas et al. 2007 Schafer et al. 2019 Li et al. 2021 Besbes et al. 2015 Darmana et al. 2007 Besbes et al. 2020 Experiments - - - - - - - - - Global holdup - - - - - - - - - Local holdup - - - - - - - - - Liquid velocity - - - - - - - - - Wall effects - - - - - - - - - Turbulent kinetic energy - - - - - - - - - Turbulent dissipation rate - - - - - - - - - Global Sauter diameter - - - - - - - - - Local diameter distribution - - - - - - - - - Local Sauter diameter - - - - - - - - - Reactions - - - - - - - - - Heat transfer - - - - - - - - -

界面浓度传输方程

数量密度函数$n(V)$方程（单位$1/m^6$）：
\begin{equation}
\frac{\p n}{\p t}+\nabla\cdot{(n\bfU)}=S_{bre}+S_{coa}
\end{equation}
定义矩：
\begin{equation}
m_k=\int V^kn\rd V
\end{equation}
因此$m_0$表示每单位体积的粒子数量，$m_1$表示每单位体积的粒子体积，也即相分数$\alpha$。因此有体积传输方程：
\begin{equation}
\frac{\p m_1}{\p t}+\nabla\cdot{(m_1\bfU)}=\int VS_{bre}\rd V+\int VS_{coa}\rd V
\end{equation}
由于体积守恒，因此其中
\begin{equation}
\int VS_{bre}\rd V+\int VS_{coa}\rd V=0
\end{equation}
在下文中我们用$\alpha$表示一阶矩$m_1$，因此有：
\begin{equation}
\frac{\p \alpha}{\p t}+\nabla\cdot{(\alpha\bfU)}=0
\end{equation}
即相方程。定义$A(V)$为体积$V$粒子的表面积：
\begin{equation}
A=\pi d^2, V=\frac{\pi d^3}{6}
\end{equation}
有：
\begin{equation}
A(V)=6^{2/3}\pi^{1/3}V^{2/3}
\end{equation}
同时定义界面浓度$a$：
\begin{equation}
a=\int A(V)n\rd V
\end{equation}
依据矩关系：
\begin{equation}\label{AV}
A(V)=\frac{\int A(V)n\rd V}{\int n\rd V}=\frac{a}{m_0}
\end{equation}
\begin{equation}\label{V}
V=\frac{\int Vn\rd V}{\int n\rd V}=\frac{\alpha}{m_0}
\end{equation}
有：
\begin{equation}
\frac{\p a}{\p t}+\nabla\cdot{(a\bfU)}=\int A(V)S_{bre}\rd V+\int A(V)S_{coa}\rd V
\end{equation}
由于粒子界面不具有守恒性，因此
\begin{equation}
\int A(V)S_{bre}\rd V+\int A(V)S_{coa}\rd V \neq 0
\end{equation}
同时依据\eqref{AV}和\eqref{V}的关系有：
\begin{equation}
A=\frac{a}{m_0}=6^{2/3}\pi^{1/3}\frac{\alpha}{m_0}^{2/3} \rightarrow m_0=\psi\frac{a^3}{\alpha^2},A=\frac{1}{\psi}\left(\frac{\alpha}{a}\right)^2
\end{equation}
其中
\begin{equation}
\psi=\frac{1}{36\pi}
\end{equation}
依据积分关系：
\begin{equation}
\begin{split}
\int A(V)S_{bre}\rd V \approx \Delta A\int S_{bre}\rd V,
\\
\int A(V)S_{coa}\rd V \approx \Delta A\int S_{coa}\rd V
\end{split}
\end{equation}
Ishii在2004年中的文章中假定
\begin{equation}
\Delta A=\frac{1}{3}A,
\end{equation}
这是因为考虑聚并和破碎的情况下，粒子界面变化分别为：
\begin{equation}
\Delta A=-0.413A, \Delta A=0.26A
\end{equation}
其中$|0.413|+|0.26|\approx 1/3$。因此，有：
\begin{equation}\label{S}
\begin{split}
\Delta A\int S_{bre}\rd V=\frac{1}{3}A\int S_{bre}\rd V
\\
\Delta A\int S_{coa}\rd V=\frac{1}{3}A\int S_{coa}\rd V
\end{split}
\end{equation}
在IATE算法中，通常将方程\eqref{S}中的积分表示为
\begin{equation}\label{R}
\int S_{bre}\rd V=R_{bre},\int S_{coa}\rd V=R_{coa}
\end{equation}
这样有：
\begin{equation}
\frac{\p a}{\p t}+\nabla\cdot{(a\bfU)}=\frac{1}{3} \frac{1}{\psi}\left(\frac{\alpha}{a}\right)^2 (R_{bre}+B_{coa})
\end{equation}

聚并破碎源项

如果只是查看，emacs 有个 whitespace mode。
空格、tab、换行之类的特殊字符都可以显示
vim按说应该也有，没搜到

Screenshot from 2021-05-22 15-16-48.png

Latex安装方法?

在线的不香吗? 小白用在线编辑 https://www.overleaf.com/

在OpenFOAM文件家下打开终端输入

find src applications -name "*.L" -type f | xargs sed -i -e 's=\(YY\_FLEX\_SUBMINOR\_VERSION\)=YY_FLEX_MINOR_VERSION < 6 \&\& \1='

ipmitool -I lan -U ADMIN -H 192.168.1.18 sensor thresh FANB lower 100 150 200 ipmitool -I lan -U ADMIN -H 192.168.1.18 sensor thresh FANB lower 0 0 0

各位简直就是大佬中的大佬 厉害厉害 :chitang:

https://askubuntu.com/questions/1143840/downgrade-openmpi-v2-1-1-to-v2-0-2

https://github.com/open-mpi/ompi/issues/6300

有空测试下

@李东岳这里提示重复定义，在59行有定义，而且和这个函数一样。 003f24ca251de51d6dbeaacef31c1ce.png

wps的国际版更干净。但是国内版的缺失字体会自动下载，国际版好像因为版权什么的，这类功能少点。不知道老师用的哪版

@李东岳 这个不是，这不是在这边下载BT什么的很危险嘛，搞了个罗马尼亚的抗版权vps 搭了一个aria2用来下载，一个季度8刀，每个月10T流量

说真的，大佬，咱能不能别3分钟限制了。。。。

捕获.JPG

最近一个月浏览量1076980

@fu 是的，老版本的要简单一些。

这个潘工的联系方式给我呀，500块买不了上当啊

感谢各位大佬！:chitang:

回档了 这是什么意思..

https://www.wikiwand.com/en/Centroid

While in geometry the word barycenter is a synonym for centroid, in astrophysics and astronomy, the barycenter is the center of mass of two or more bodies that orbit each other. In physics, the center of mass is the arithmetic mean of all points weighted by the local density or specific weight. If a physical object has uniform density, its center of mass is the same as the centroid of its shape.

ISB

https://www.isb.bj.edu.cn/admissions/life-in-beijing

不接受中国学生

BSB

https://www.nordangliaeducation.com/en/our-schools/beijing/shunyi/admissions/how-to-apply

暂时不清楚是否接受中国学生

德威

https://beijing.dulwich.org/zh/admissions

不接受中国学生

哈罗

https://www.harrowbeijing.cn/academic-cn/lower-school

貌似接受中国学生

乐成

https://bcis.openapply.cn/

接收中国学生

青苗

https://www.bibs.com.cn/chinese-home/admissions/faq1

招收中国学生

鼎石

https://www.keystoneacademy.cn/

招收中国学生

海嘉

http://www.bibachina.org/index.html?deptId=103

招收中国学生

世青

https://www.ibwya.net/

招收中国学生

其实一楼这个问题我还是有点没想明白。就是一个x方向的一维算例，出现了y方向的速度，应该如何理解..