Chapter 736 Challenge the 15th step of the NS equation

Chapter 736 Challenging Step 1.5 of the NS Equation

After signing, Ding Gaoheng put the pen back into the pen holder. When he raised his head again, he only saw Chang Haonan leaning on the sofa, his eyes looking at the ceiling distractedly, as if he was in a state of wandering mind.

It seemed that he was thinking, so he was not in a hurry, just pushed the report to the corner of his desk, and then started to deal with other official duties.

As a result, such a strange scene appeared in the office of the director of the Science and Technology Commission.

Ding Gaoheng was crouching on the desk writing furiously, getting up from time to time to refill himself a glass of water.

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

That kind of relaxed state, if I didn't know it, I would think there was some special relationship between the two people...

Fortunately, this afternoon was unusually peaceful.

It wasn't until he was about to get off work that Chang Haonan broke away from his thoughts just now.

"Xiao Chang?"

Seeing that he finally moved, Ding Gaoheng also breathed a sigh of relief.

"Oh... Director Ding... I suddenly had some inspiration just now, and I'm thinking more clearly..."

Chang Haonan sat up straight, and at the same time, almost subconsciously, he raised his hand and stroked his forehead.

It turned out to be covered in sweat.

I'm really sweating now.

The air conditioner is naturally turned on in the office, but after all, Ding Gaoheng is old and not as physically strong as young people, so it is impossible to turn on the lowest temperature and blow it hard.

Therefore, the temperature in the room was already a bit high for Chang Haonan. Coupled with the high load of thinking just now, it did put a lot of load on 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 up to a level that Chang Haonan could accept.

Otherwise, I'm afraid it's really going to be "I'm on fire!"

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 saw it, so I didn't call you just now because I was afraid of disturbing your train of thought."

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

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

"Thank you, Director Ding."

Chang Haonan said a simple polite word, then pulled off a few pieces of paper, stacked them together and began to wipe the sweat.

"What were you thinking about just now, so lost in thought?"

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

"Well...it's about graduation thesis."

"what?"

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

"You still have to worry about your graduation thesis?"

In his opinion, Chang Haonan is now like a big father to Jinghang. It is too late to be a Bodhisattva, so how could he interfere with graduation matters.

Furthermore, given the current situation, if you target Chang Haonan, you are targeting him, Ding Gaoheng. To go even further, you are targeting...

There shouldn't be anyone so short-sighted.

"Not the thesis itself."

Chang Haonan shook his head and quickly explained:

"I just suddenly thought of some extended research from the content of my paper, about using the spatial averaging principle to correct the NS equation..."

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

After all, in the long time the two had known each other, he had never seen the other person thinking for so long.

There was no expectation of an in-depth discussion on this topic.

But the moment Chang Haonan mentioned the NS equation in his answer, he immediately became interested:

"Have you thought of a new numerical solution method?"

For anyone whose research field is related to fluids, the NS equation is a mountain that cannot be bypassed.

Since current mathematical tools cannot find strict analytical solutions, how to obtain numerical solutions to specific problems more accurately and efficiently has become the focus of applied mathematicians and physicists from all over the world.

It can be said that the TORC Multiphysics software has achieved an era-leading lead in the field of fluid calculations, largely due to the breakthroughs made by Chang Haonan in the numerical solution level at that time.

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

What's more, even the software of the professional enhanced version is not public, let alone the source code.

And if it happens again at this time...

Ding Gaoheng didn't dare to think about what would happen.

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

"not completely……"

This made Ding Gaoheng's excitement subside a little.

But think about it, a breakthrough of that level can only occur once in a few years or even more than ten years, which is already extraordinary.

Moreover, even if it is only further modified at the level of the original algorithm, the calculation efficiency can be significantly improved...

"I believe that the inertial manifold of two-dimensional NS equations exists universally."

Chang Haonan's second sentence choked back Ding Gaoheng's words.

"what?"

The latter's mind couldn't keep up for a while.

"The inertial manifold of two-dimensional NS equations may exist universally."

Chang Haonan repeated it.

But it is obvious that Ding Gaoheng did not understand the Chinese characters clearly, but he heard each word, but did not understand the meaning of the words.

So he had no choice but to explain:

“Simply put, because there is an affinity relationship between fast variables and slow variables, directly ignoring the fast variables and retaining the slow variables will lead to the loss of a lot of dynamic information in the process of dimensionality reduction of the nonlinear partial differential equation system. . Including my current research, the function of all nonlinear dimensionality reduction methods is to improve the modeling accuracy without increasing the dimensionality of the reduced system, to compensate for part of the lost information. "

"The inertial manifold is one of them, but because in the inertial manifold, the ignored fast variables can be represented by slow variables, the calculation accuracy and efficiency are much higher than the traditional methods in the past... But for For most nonlinear partial differential equations, including NS equations, it is difficult to find the corresponding inertial manifold..."

"So we, uh...that is, the TORC 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 pattern can easily obtain an approximate inertial flow pattern by ignoring the dynamic information of the fast variable; the second is to Considering the dynamic information lost by deleting fast variables, and using the Euler method to calculate the integral of the deleted fast variables in a short time interval, an approximate inertia manifold can still 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 have returned to the category of pure applications and are not very helpful in advancing theoretical research. …”

"..."

Ding Gaoheng did not have a background in mathematics, not to mention that what Chang Haonan said was not even applied mathematics, but was already a bit 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, the general meaning is still understandable:

"So...you want to...obtain the global solution to the NS equation?"

This idea is a bit too unrestrained——

If the NS equation is really completely cracked, it will basically be equivalent to reshaping the entire aerospace industry from its roots.

What wind tunnel, what aerodynamic verification machine...

Not needed at all.

Just put it into prototype and put it into production.

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

Chang Haonan quickly waved his hand:

"Although in terms of direction, it can indeed be said that it has taken a step towards solving the NS equation, but the distance from truly obtaining an analytical solution can only be regarded as the first step in the long march..."

Speaking of this, he hesitated again:

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