Chapter 736: Step 15 of Challenging the NS Equation

Chapter 736 Step 1.5 of the Challenge of the N-S Equation

After signing, Ding Gaoheng put the pen in his hand back into the pen holder. When he looked up again, he saw Chang Haonan leaning on the sofa, looking at the ceiling with a distracted look, as if he was in a trance.

He seemed to be thinking, so he was not in a hurry. He just pushed the report to a corner of the desk and started to deal with other official business.

So, such a strange scene appeared in the director's office of the Science and Technology Commission.

Ding Gaoheng was writing furiously at the desk, and he got up from time to time to refill himself with a glass of water.

And on the sofa not far away, there was a young man sitting with his eyes looking up at the sky...

If someone didn't know that kind of relaxed state, they would think there was some special relationship between the two people...

Fortunately, this afternoon was unusually calm.

It was not until the end of get off work that Chang Haonan broke away from his thoughts just now.

"Xiao Chang?"

Seeing him finally move, Ding Gaoheng also breathed a sigh of relief.

"Oh... Director Ding... I just had some inspiration and was lost in thought..."

Chang Haonan sat up straight and raised his hand almost subconsciously to stroke his forehead.

It turned out that it was covered with sweat.

Really sweating.

The office was naturally air-conditioned, but Ding Gaoheng was not young after all, and his physique was not as good as that of young people, so it was impossible to turn it on at the lowest temperature.

Therefore, the temperature in the room was a bit high for Chang Haonan, and the high-load thinking just now did bring a lot of load to the body temperature regulation mechanism.

Fortunately, the system should have the ability to automatically adjust. Except for the first moment, the "computing power" was always turned on to a level that Chang Haonan could accept.

Otherwise, I'm afraid I'll really "burn up!".

But this also gave Chang Haonan a new idea-

If he really soaked in a bathtub of ice cubes, would his thinking efficiency be further improved...

"I noticed it, so I didn't call you just now because I was afraid of disturbing your thoughts."

Ding Gaoheng obviously saw the sweat on Chang Haonan's face, and stood up and put a roll of paper on the coffee table:

"Wipe your sweat, the weather at the end of May is already a bit hot..."

"Thank you, Director Ding."

Chang Haonan said a simple polite sentence, then tore off a few pieces of paper and stacked them together to start wiping his sweat.

"What were you thinking about just now, so absent-minded?"

Ding Gaoheng returned to his seat and asked casually while blowing gently on the teacup.

"Well... graduation thesis."

"Ah?"

On the other side, Ding Gaoheng stopped fiddling with the cup lid and raised his head in shock:

"You still need to worry about graduation thesis?"

In his opinion, Chang Haonan is now like a big dad to Jinghang. He is too busy worshipping him like a Buddha, so how could he mess with graduation.

Besides, in the current situation, targeting Chang Haonan means targeting him, Ding Gaoheng, and to put it more deeply, targeting...

No one should be so blind.

"Not the graduation thesis itself."

Chang Haonan shook his head and explained quickly:

"Just now, I suddenly thought of some extended research from the content of my thesis, about using the spatial average principle to correct the N-S equation..."

In fact, Ding Gaoheng just asked casually out of curiosity at first.

After all, since the two of them knew each other for such a long time, he had never seen the other person thinking for such a long time.

He did not expect to have an in-depth discussion on this topic.

But when Chang Haonan mentioned the N-S equation, he immediately became interested:

"Have you come up with a new numerical solution method?"

For anyone whose research field is related to fluid, the N-S equation is a mountain that cannot be bypassed.

Since current mathematical tools cannot find strict analytical solutions, how to obtain numerical solutions for specific problems more accurately and efficiently has become the focus of attention of applied mathematicians and physicists in various countries.

It can be said that the TORCH Multiphysics software can achieve a cross-era lead in the field of fluid calculation, largely due to the breakthrough made by Chang Haonan in the numerical solution level at that time.

Although part of the mathematical theory is a public achievement, when it comes to the application level, even if others use the source code to compare, it is difficult to keep up with the pace of optimization and iteration of the Torch Group itself.

What's more, the professional upgrade version is not even open to the public, let alone the source code.

And if it happens again at this time...

What will happen, Ding Gaoheng dare not think.

However, Chang Haonan's response is to shake his head:

"Not entirely..."

This made Ding Gaoheng's excitement subside a little.

But think about it, a breakthrough of that level is already very remarkable if it happens once every few years or even more than ten years.

Moreover, even if it is only further modified at the level of the original algorithm, it can also significantly improve the computing efficiency...

"I think the inertial manifold of the two-dimensional N-S equation is universal."

Chang Haonan's second sentence choked back the words that Ding Gaoheng had already said.

"What?"

The latter's brain was a little slow to catch up for a while.

"The inertial manifold of the two-dimensional N-S equation may be universal."

Chang Haonan repeated it.

But it is obvious that Ding Gaoheng did not fail to hear the Chinese characters clearly, but heard every word but did not understand the meaning of the connection.

So he had to explain:

"In simple terms, because there is an affinity between fast variables and slow variables, directly ignoring fast variables and retaining slow variables will lead to the loss of a lot of dynamic information in the process of reducing the dimension of the nonlinear partial differential equation system. And including my current research, the role of all nonlinear dimensionality reduction methods is to improve the modeling accuracy without increasing the dimension of the system after dimensionality reduction, which is used to compensate for some lost information."

"Inertial manifold is one of them, but because in the inertial manifold, the ignored fast variables can be represented by slow variables, so the calculation accuracy and efficiency are much higher than the traditional methods in the past... It's just that for most nonlinear partial differential equations, including N-S equations, it is difficult to find the corresponding inertial manifold..."

"So we, uh... that is, TORCH Multiphysics software currently uses two methods. One is to assume that the fast variable is in a pseudo-stable state, so that the stable flow type can easily obtain an approximate inertial flow type by ignoring the dynamic information of the fast variable; the other is to consider the dynamic information lost by deleting the fast variable, and use the Euler method to calculate the integral of the deleted fast variable in a short time interval, and an approximate inertial manifold can also be obtained..."

"However, both methods are essentially superimposed approximations on the basis of approximations, so although the results are indeed better than the traditional methods, they return to the scope of pure application, which is not very helpful for promoting theoretical research..."

"..."

Ding Gaoheng is not a mathematician, not to mention that what Chang Haonan said is not even completely applied mathematics, but has already moved towards the theoretical part, so after listening to it, he just felt...

This "simply put" is not simple.

However, although I didn't fully understand the specific content, I could still understand the general meaning:

"So... you want to... get the global solution of the N-S equation?"

This idea is a bit too self-indulgent-

If the N-S equation is really completely cracked, it is basically equivalent to reshaping the entire aerospace industry from the root.

What wind tunnel, what aerodynamic verification machine...

All are not needed.

Just go straight to the prototype and put it into production.

"Ah... no, no, no, it's not that exaggerated."

Chang Haonan waved his hand quickly:

"Although in terms of direction, it can be said that it has taken a step towards solving the N-S equation, but it can only be regarded as the first step of a long march to truly obtain an analytical solution..."

Speaking of this, he hesitated again:

"It's not just the first step. After all, it is a step forward on the basis of pure numerical solution, but the second step is a bit... Strictly speaking, it's the 1.5th step..."