Chapter 736 Challenge the N-S Equation Step 1.5
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 He stared at the ceiling distractedly, as if he was in a state of wandering mind.
Looking at this posture, he seemed to be 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.
So, 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 he didn't know it, he would think there was something special between the two people. Relationship...
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...just suddenly had some inspiration, and he was thinking more clearly..."
Chang Haonan sat up straight and raised his hand almost subconsciously, He 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" has been turned up to a level that Chang Haonan can accept.
Otherwise, I’m afraid it will really “ignite me!”.
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 also obviously saw the sweat on Chang Haonan's face. He stood up and put a roll of paper on the coffee table:
"Wipe the 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, folded 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 the graduation thesis."
"Huh?"
On the other side, Ding Gaoheng stopped fiddling with the lid of the cup and raised his head in shock:
“Are you still worrying about your graduation thesis?”
In his opinion, now Chang Haonan is 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. Going even further, you are targeting...
There should be no one who is so short-lived. Eyes are right.
"It's not the graduation thesis itself."
Chang Haonan shook his head and quickly explained:
"I just suddenly came up with some extended research from the content of my thesis, about using The principle of spatial averaging corrects the N-S equation..."
In fact, Ding Gaoheng just asked casually out of curiosity at first.
After all, since the two people have known each other for such a long time, he has 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 N-S equation in his answer, he immediately became interested:
“Have you thought of a new numerical solution method again?”
For anyone whose research field is related to fluids, 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 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 TORCH 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 is a public achievement, at the application level, 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 the 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 doesn't even dare to think about what will happen.
However, Chang Haonan's response was to shake his head:
"Not exactly..."
This made Ding Gaoheng's excitement subside a little.
But think about it, a breakthrough of that level can only happen 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 the two-dimensional N-S equation exists universally."
Chang Haonan's second sentence choked Ding Gaoheng's words back.
“What?”
The latter’s mind couldn’t keep up for a while.
“The inertial manifold of the two-dimensional N-S equation 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 connection.
So he had to explain:
"To put it simply, because there is an affinity relationship between fast variables and slow variables, the fast variables are directly ignored and the slow variables will be retained. As a result, a lot of dynamic information is lost in the process of dimensionality reduction of nonlinear partial differential equation systems. Including my current research, the function of all nonlinear dimensionality reduction methods is not to increase the dimensionality of the system after dimensionality reduction. Improve the modeling accuracy on the premise of compensating 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 slowed down. The variables are expressed, so the calculation accuracy and efficiency are much higher than the traditional methods in the past... However, for most nonlinear partial differential equations, including N-S 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..."
"There are only two methods. Essentially, they are all superimposed on the basis of approximation, so although the results are indeed better than the traditional method, it has returned to the category of pure application, which is not very helpful in advancing theoretical research..."
"..."
Ding Gaoheng is not a mathematician, not to mention what Chang Haonan said is not even completely applied mathematics, but has already moved towards the theoretical part, so he After listening to it, I just felt...
This "in simple terms" is not simple.
However, although I did not fully understand the specific content, the general meaning is still understandable:
"So...you want to...obtain the global solution of the N-S equation?"
This The idea is a bit too unrestrained -
If the N-S equation is really completely cracked, it will basically be equivalent to reshaping the entire aerospace industry from the root.
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 is towards solving N-S The equation has taken a step forward, but it is still only the first step in the 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... strict. Let’s talk about step 1.5..."
(End of this chapter)