The military-industrial scientific research system of the academic master.

In the email just sent by Maryam Mirzakhani, the idea of ​​"reversely using humans to prove the Poincare conjecture" was mentioned.

But in fact, if we have to say, the level set method is closer to the reverse manifold learning algorithm.

Of course, this is not actually the case; it is just a way of summarizing the idea.

Manifold learning algorithms process high-dimensional data into low dimensions, making it easier for humans to understand.

The level set method projects low-dimensional data into high dimensions to facilitate computer calculations.

In the field of numerical computing, this is considered a "new" algorithm that was only proposed in the late 80s. However, because its application range includes but is not limited to liquid atomization, evaporation, combustion, surface material calculation, image recognition... In short, it is almost all-encompassing like manifold learning, so it was quickly extended to various fields.

Including TORCH Multiphysics, several typical level set methods were also introduced in the official version.

But the problem is that the current level set method, even after improvement, can only achieve "approach" conservation within a specific range.

This is a very troublesome problem.

This is especially true in its main application area - two-phase flow calculation.

Because in most cases, the two fluids involved in two-phase flow problems can be considered immiscible, which means that the method used must effectively maintain the conservation of mass of each phase.

Therefore, the current level set algorithm is prone to violent oscillation and even divergence in long wheelbase time calculations.

This should be the part that the level set algorithm is best at.

For example, in the process of designing the combustion chamber of the WS-10 engine, Chang Haonan combined the fluid volume method and the level set method to calculate the diffusion behavior of aviation fuel after leaving the atomizing nozzle.

What is the result...

Useful, but not much.

Compared to the relatively “simple” single-phase flow calculations for the compressor and turbine sections, the project team received minimal guidance during the design of the combustor and was forced to use the old method of combining a lot of experience with pilot tests.

This also results in more than 60% of the time and money in component-level testing being spent on this.

Fortunately, thanks to the limited volume of the small bypass ratio aircraft engine combustion chamber itself, the diffusion process does not last particularly long, so the calculation results will not fluctuate too much. In addition, the performance indicators pursued by the WS-10 are relatively low compared to its superior overall design, so it did not affect anything in the end.

But if we pursue larger models with more advanced data in the future, such as a behemoth like GE9X.

Or another application scenario, rocket engine——

Whether liquid fuel or solid fuel, since rocket engines have to carry all of their own propellants, their reliance on the combustion-injection process is far greater than that of aircraft engines.

So this conservation problem still needs to be solved.

Of course, since the title of this paper is “A method of…”, it means that it is definitely not a theoretical solution to both the symptoms and the root causes.

It is only applicable in certain specific application scenarios.

However, even so, it is a huge improvement over the current level set methods.

[…This paper proposes a class of conservation level set methods for dealing with two-phase flow problems with divergent free velocity fields, and in the process develops an efficient method for dealing with Robin boundary conditions on irregular interfaces. Combined with the phase change solution method of interface analysis, the effects of liquid shape and internal circulation on heat and mass transfer are considered…]

[First, assume an arbitrary region w, and its subregion 2=w/w1. Γ is the interface that divides w, and a regularization function Φ (usually a smooth Heaviside function) is constructed to implicitly represent Γ, so that when passing through Γ, Φ changes rapidly from 1 to 0, and in the subregion w1, Φ≈1, and in the subregion w2, Φ≈0, so Γ is generally set to the 0.5 level set of Φ. In the calculation, we hope to maintain the shape of the interface even in the presence of small perturbations...]

【…】

Time passed quickly as Chang Haonan's hands typed quickly on the keyboard.

However, after about twenty minutes, Chang Haonan stopped typing.

After a little thought, he pulled out a floppy disk, copied the document he had just started into it, then stood up and went straight to the computer room.

In fact, the method he developed is not mathematically complicated. It is essentially a reinitialization process that repairs the ψ value in the level set equation by solving a stable solution to a viscosity term to achieve the purpose of maintaining conservation.

The reason why no one has ever touched upon it in the past is that it is difficult to implement in terms of specific calculation methods.

For example, the traditional grid division method is difficult to adapt to the rapidly changing two-phase fluid on the Cartesian grid.

But for Chang Haonan, who first pointed out his expertise in numerical calculation after his rebirth and also led the TORCH Multiphysics software development and algorithm design throughout the process, this was not a problem.

According to his estimation, after the introduction of the finite element discretization method with adaptive grid, the computational efficiency can still be basically guaranteed.

However, if you want to operate it in a simple form of interactive graphical interface rather than autonomous programming, you will probably have to wait until the next major version update of TORCH Multiphysics...

But...

“This is a good opportunity.”

Chang Haonan, who was typing code according to the contents of the paper, thought to himself.

Almost three and a half years have passed since the initial trial release of TORCH Multiphysics.

As for software, as long as you sell it, the code cannot be hidden anyway.

Even though Chang Haonan created three versions with different thresholds, he could only delay the process to a certain extent.

After all, there are tens of thousands of people who have access to the professional upgraded version of the software. With such a large base, it is to be expected that the news will leak out.

Furthermore, competitors are not just there to do nothing.

In short, starting around 2000, software such as Materials Studio, ANSYS Fluent, COMSOL Multiphysics, etc. have also begun to catch up in computing efficiency and performance. Although they are still far from the pioneer TORCH Multiphysics in terms of comprehensive performance, they are already qualified to compete in their respective fields of expertise.

Although the latter still firmly holds the top spot in market share thanks to its wide-ranging network over the past few years and the numerical computing services provided by Torch Group, its advantage will definitely become smaller and smaller in the long run.

Therefore, the work plan submitted by Torch Group in February included a new major version update that was expected to be launched at the end of 2 or the beginning of 2001.

This is a good opportunity to introduce Cartesian grids and this new type of level set method.

"It's time to let you feel fear again..."

Chang Haonan pressed the enter key with a click, then leaned back in his chair, looked at the calculation process displayed on the screen, and muttered to himself.

However, at this moment, a curious female voice suddenly came from not far behind him:

"Uh...what fear?"

At that moment, Chang Haonan felt his blood run cold.

Five years have passed since his rebirth, and he only acted unconsciously like a middle school student once, and he was caught red-handed.

Don’t ask, the answer is that a man remains a boy until he dies.

Chang Haonan tried his best to suppress his serious expression and turned around.

I saw Yao Mengna, wearing a light pink sweater, walking in from the door.

Fortunately.

At this distance, she should have only heard a few words.

"nothing."

Chang Haonan replied calmly:

"I mean, we shouldn't be afraid just because the research direction is difficult."

"Well... that's right."

As expected, Yao Mengna didn't understand what was going on and was easily put off.

Moreover, he then took the initiative to change the topic:

"I just came back from the cafeteria, but I couldn't see you in the office, so I guessed you were in the computer room."

"The lunch box is on the door handle of your office. Don't forget to eat when you're done."

This scene suddenly reminded Chang Haonan of the first time he saw Yao Mengna after he was reborn.

It was in the old computer room, and everyone also had lunch boxes together.

However, the lunch box seemed to be bought by Zhang Man at that time...

For a moment, Chang Haonan couldn't help but fall into memories.

"Professor Chang?"

Yao Mengna looked at Chang Haonan, whose eyes were suddenly absent-minded, and called out to him tentatively.

"Oh……"

Chang Haonan suddenly woke up and immediately glanced at the computer that was calculating.

It may take some time for the results to come out.

"Forget it, let's go eat now..."

After saying that, he stood up, put on his clothes, and left the computer room with Yao Mengna.