"Regarding the derivation of continuity equations, I personally think that the more natural way of derivation is to use the material conservation of material described by Euler and the number of derivatives."
"Consider the change of density in a region Ω in space. Since the region we choose does not change with time, that is, it is described by Euler, physics is a differential with respect to time and does not contain a random term, that is to say These physical quantities are regarded as functions about spatial coordinates rather than functions about fluid particles. ”
"So due to the conservation of matter, the change in mass in the region is equal to the difference between the mass entering the boundary and the mass left out, so..."
Wang Donglai said while writing the formula he derived on the writing board.
As for everyone in the audience, they all looked attentive at the moment, not daring to blink for fear of missing the crucial moment.
After all, this is the N-S equation!
The importance is much more important than other mathematical problems.
"Adopt Gauss's formula on the right end of the equation, and take into account the arbitrariness of the integral region, and formalize the integral into a differential form..."
"This is the form of a copy of the continuity equation. Considering that the relationship between the number of derivatives and the non -casual derivative, the continuity equation can also be turned into ..., the definition of the fluid cannot be compressed ..., for non -compressed fluid, continuity is continuous, continuity The equation becomes ... "
"Note!"
Wang Donglai tapped the writing board lightly, and a buzzing sound came from the microphone, attracting everyone's attention.
"The DP/DT inside is for the gauge mass of the germ, that is, for a certain mass point, its density does not change with time, but it does not mean that the density of different mass points is equal. If you put it, the fluid density field is constant at any time in the whole space.
"..."
"Considering the Lagrangri description of the speed field and density field, one area ω is still selected at this time. Due to the use of the Lagrangri description, the area can be regarded as a fluid micro group that changes over time. At this time, you need to consider it to consider The number of material points. "
"From the dynamic theorem, the amount of momentum changes in the volume micro group in the unit time should be equal to the sum of the physical charge of the fluid micro -group inside the entire internal."
"..."
"When constructing an energy equation, it is still necessary to use Laglangri description. According to the conservation of energy, the total energy changes of the material micro group ω are equal to the sum of external work and heat transfer."
"Note that in a general situation, the heat transfer rate K is a second -order tensor. Only under the conditions of the same sex can be regarded as a scalar ..."
There is generally a law in the academic world.
That is, there is a certain correlation between academic research ability and physical fitness.
If you have a good physical fitness, you may not have a strong academic research ability, but if you want to make academic achievements, a strong and strong body is necessary.
Just like this moment.
The proof of the N-S equation cannot be explained clearly in just a few words.
Or Wang Donglai directly came up with a formula and said that this was the proof.
This is simply impossible.
In addition, Wang Donglai also needs to make the proof process as easy to understand as possible to prevent scholars present from not being able to understand it because it is too complicated.
In this way, the proof of the process naturally becomes extremely cumbersome.
However, even though Wang Donglai tried his best to keep it simple, it was still beyond the acceptance range of many scholars present.
Without even asking for half an hour, almost a hundred scholars had already fallen behind and could not keep up with Wang Donglai's ideas.
At this time, the gap can also be clearly seen.
The vast majority of scholars who are the first to be left behind are professors from domestic universities.
This thing cannot be avoided.
Since this academic exchange meeting was put on the Tang Dynasty Jiaotong University, and the theme was proposed by Wang Dong.
The State of China is naturally the well-deserved host, and Tangdu Jiaotong University also holds the quota of participants.
This venue was renovated by Tang Dujiao.
When Wang Dong came to the graduation thesis defense before, Tang Du Jiaotong University gave birth to this idea.
Sure enough, within two years, it was put to use.
The super conference venue, which can accommodate thousands of people, can no longer be said to be an academic exchange conference. It can almost be said to be a mathematician conference.
Among the following scholars, there are not many scholars from overseas, accounting for only about one -fifth of the total number.
The remaining places were given by Tangdu Jiaotong University to major domestic universities and research institutes.
Wang Donglai also understood this incident and did not refuse.
Leaving a large number of places for domestic scholars and enthusiasts is actually what he wants to do.
If the mathematics major of Hua Guo wants to develop, it is impossible to rely on one person alone.
Even Wang Donglai single-handedly pushed mathematics to a new level.
But if there is no successor and inherit these knowledge, it is quite the air tower. Without the foundation, a slight storm will collapse.
Wang Dong does not do such a thing, let alone allow such things to happen.
However, he understands that mathematics is really talented.
If it works, it works. If it doesn't, it doesn't work.
There is almost no talented scholar. After hard study research, what major scientific research is found.
Half an hour passed!
An hour passed!
Wang Donglai has already filled three writing boards with various mathematical symbols.
It's like English.
As for the scholars who could follow Wang Donglai's ideas and persist until this point, there were not many scholars left.
Whether or not scholars who can keep up with Wang Donglai's thinking are similar at this moment.
Either he is recording an important node with a pen, or it is calculated on the draft paper.
Even though Wang Donglai deliberately slowed down the speed and broke down some links in detail, the N-S equation was still too difficult.
Therefore, many scholars simply cannot keep up with the pace.
I can only prove it from where I can't keep up with the rhythm, and I want to continue thinking along Wang Donglai's train of thought.
For top mathematicians like Tao Zhexuan, Deligne and Qiu Chengtong, the situation is different.
The more he listened to Wang Donglai, the more people's eyes became brighter.
Several people can become the world's top mathematicians, one is talent, the other is diligence and persistence, and finally the love of mathematics from the heart.
The three are indispensable, and no one can become the top mathematician.
Therefore, in the hearts of the three, according to the proof procedures and data from the current Wang Donglai, Wang Dong has been able to prove the N-S equation.
However, the three did not tell their judgments directly before they heard the end and after inspection.
This happens many times in mathematics.
Obviously all the steps were correct, but at the last step, an incorrect result was obtained, causing the previous work to be wasted.
Deligne and others have seen many such things.
Therefore, no matter how confident Wang Donglai is in his heart, it will not be manifested obviously, and it will not express before the result comes out.
Some scratched their heads, some frowned, and some looked happy. Of course, there are also people with dark faces.
It was a few people who had trouble before.
Originally, in accordance with Huang Yun's instructions, it was prepared to directly drive the security personnel to drive these people out.
But since Wang Donglai said that, Huang Yun naturally gave up this idea, but left a few people to stay.
Several people can mix in, and they have a bit of ability.
With anger towards Wang Donglai in my heart, when Wang Donglai was proving, I pricked up my ears and listened attentively, hoping to find Wang Donglai to prove the problems in the process.
One million is not a small, but for them, it is nothing.
What they care about is that as long as they can find Wang Dong to prove the process, they can play to promote Wang Donglai's proof.
However, no matter how hard they tried, they could not find any problem, and their faces gradually became ugly.
"Can Wang Donglai really prove the N-S equation?"
As soon as this idea emerged in the hearts of several people, it was beaten up by several people.
There is no mistake, one, one, one, one, one, one, one, one 619, one book, one, one, one, one, one, one, a book!
It is not that they feel impossible, but because they are unwilling to believe this, they are unwilling to accept this fact, they can only choose self -paralysis.
Time is still passing by.
Two hours!
Three hours!
Even scholars sitting below couldn't sit still.
It's not that they can't sit still, but that high-intensity thinking puts a heavy burden on the body.
In addition, most of the scholars are in their fifties, and even if there are some who are slightly younger, the average age is still in their early fifties.
This age is no longer young, and the three -hour uninterrupted high -intensity thinking has made many people feel a little unable to persist.
only.
Wang Donglai on the stage didn't mean to stop.
Once the writing board is full, it is hung up and replaced with a new one.
Earlier, Tang Dujiao was reminded by Wang Donglai, so he was well prepared.
Before Wang Donglai said that the proof was over, it was impossible for everyone to leave early.
Since you have come to participate in this academic exchange conference, you must persist until the end.
"The governing equations of fluids in CFD can have a variety of mathematical expressions, such as conservation type and non-conservation type. These expressions have common physical principles and can be converted into each other. However, when using different numerical methods to solve, Choosing an appropriate equation form can give a reasonable solution, otherwise problems such as non-physical solution and instability may occur. ”
"Therefore, when learning the basic equations of CFD, you must figure out how these equations are derived from, where are their similarities, what are the differences, and how to transform each other."
"The derivation of the fluid mechanics equation is based on the continuous media assumption. This assumption ignores the distance between fluid molecules, and the fluid is regarded as a continuous, non -gap full space."
"In addition, the internal parts of the fluid can have different velocities when moving, and it is difficult to maintain a fixed shape, so to describe the movement of the fluid we need to choose and appropriate models..."
"With fluid microelements as the research object, differential equations will be derived."
"With the finite control volume as the research object, the integral equation will be derived. The difference between the two is that the integral equation allows discontinuities in the control volume, while the differential equation requires the flow field variables to be continuously differentiable because it involves the concept of limits."
"The constant -oriented equation derived by Euler France is derived from the non -conservation equation derived by Lagram."
"..."
"The N-S equation, as a non-linear partial micro-division equation, is quite complicated and has the characteristics of different solutions in different situations. It is difficult to describe the current mathematical language."
"If you must write it, the way of resolving the interpretation is probably a form of infinite level."
"In order to give everyone a clearer understanding, I have simplified it a bit."
Wang Donglai did not return. While writing a long mathematical formula on the writing board, he said calmly.
And when he heard Wang Donglai, everyone's expression was different.
Wang Donglai's words were almost as clear as saying that they were idiots.
If you change the place, change the time, and change the person, everyone will never be the calm look at the moment.
However, at this moment, the person said that was Wang Donglai.
He is the world's top mathematician who is proving the N-S equation!
As for their academic level, they had already noticed it when Wang Dong came to explain.
Therefore, Wang Dong is not wrong.
They are indeed not in place.
Even the proof process that Wang Donglai had simplified was quite difficult for them at this moment.
When everyone was thinking so.
Wang Donglai also wrote the final mathematical formula on the writing board.
"The above is all my proof procedures."
Wang Dong turned back and forth, looking at a calm and calm appearance, looking at thousands of scholars and professors under the audience, and said confidently.
Although there is only such a sentence, everyone present can understand that Wang Donglai still has a sentence that has not been said.
That is: "The N-S equation has been proved by me. From now on, there is one less mathematical problem!"
After a few breaths.
Everyone in the entire venue stood up in unison, stretched out their hands and clapped.
"Pa bang bang..."
Applause is like a thunderous, and the mountains fall.
Although it is still not possible to completely verify whether there are any problems with Wang Donglai's proof and whether it really proves the N-S equation, what they learned when Wang Donglai proved it is enough for them to applaud and express their gratitude.
The applause has not stopped, and it lasts for three minutes.
The front desk cameraman who stayed at the venue also captured several very impactful photos.
In the atmosphere of excitement in the audience, there was a little inconsistent place.
Those were the people who had stood up to question Wang Donglai before, and their faces were extremely ugly at this time.
They could not understand all the proofs of Wang Donglai, nor did they find the problem of Wang Donglai's proof.
Therefore, they dare not say whether this mathematical problem has been proven.
"This proof process has not been checked yet, it cannot be said that the N-S equation has been proved!"
Soon, several people thought of this and shouted loudly.
In this way, it suddenly attracted a lot of bad eyes. (End of this chapter)