Chapter 897 It’s Time to Bring some Small Shocks to the Industry Again

Chapter 897 It's time to bring some small shocks to the industry again...

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

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

Of course, it is not actually the case, but it can be summarized in this way.

The manifold learning algorithm processes high-dimensional data into low dimensions to make 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 a "new" algorithm that was only proposed in the late 1980s, but 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 introduced in the official version.

But the problem is that the current level set method, even after improvement, can only achieve "close" 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 the two-phase flow problem can be regarded as immiscible, which means that the method used must effectively maintain the conservation of the mass of each phase.

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

and this should be the part where the level set algorithm is best at.

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

The result...

Useful, but not much.

Compared with the relatively "simple" single-phase fluid calculations of the compressor and turbine parts, the project team received the least guidance in the design of the combustion chamber and was forced to use the old method of combining a lot of experience with pilot tests.

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

Fortunately, thanks to the limited volume of the combustion chamber of the small bypass ratio aircraft engine, the duration of the diffusion process is not particularly long, so the calculation results will not fluctuate too much, and 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 and more advanced models in the future, such as the behemoth GE9X.

Or another application scenario, rocket engines-

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

Then this conservation problem still needs to be solved.

Of course, since the title of this paper is called "a method of...", it means that it is definitely not a theoretical solution.

It is only applicable in certain specific application scenarios.

However, even so, it is a huge improvement for the current level set method.

【…This paper proposes a class of conservation level set methods for two-phase flow problems with divergent free velocity fields, and in the process develops an efficient method for handling Robin boundary conditions on irregular interfaces, combining the phase change solution method of interface analysis to consider the effects of liquid shape and internal circulation on heat and mass transfer…】

【First, assume an arbitrary region Ω, and its subregions Ω1 and Ω2, and Ω2=Ω/Ω1. Γ is the interface that divides Ω, 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 Ω1, Φ≈1, and in the subregion Ω2, 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 disturbances…】

【…】

Time passed quickly as Chang Haonan's hands quickly tapped 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 written, and then stood up and went straight to the computer room.

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

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

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

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

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

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

But...

"This is also a good opportunity."

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

It has been almost three and a half years since the initial trial version of TORCH Multiphysics was released.

As for software, as long as you sell it, the code can't be hidden anyway.

Even if Chang Haonan made three versions with different thresholds, it can only delay this process to a certain extent.

After all, there are tens of thousands of people who can access the professional upgraded version of the software. After the base number is large, it is expected that the news will leak out.

In addition, the competitors in the same industry are not just for free after all.

In short, since around 2000, software such as Materials Studio, ANSYS Fluent, COMSOL Multiphysics, etc. have also begun to catch up in terms of 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 occupies the top spot in market share by relying on the wide-ranging network in the past few years and the numerical computing services provided by Torch Group, the advantage will definitely become smaller and smaller in the long run.

Therefore, the work plan submitted by Torch Group in February includes a new major version update that is expected to be launched at the end of 2001 or the beginning of 2002.

It is just right to introduce Cartesian grids and this new type of level set method.

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

Chang Haonan pressed the enter key with a snap, then leaned back in his chair, looking 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 after his rebirth, he had only unconsciously acted like a middle school student once, and he was caught red-handed.

Don't ask, the answer is that men are teenagers until they die.

Chang Haonan tried his best to hold back his serious expression, and then turned around.

Seeing Yao Mengna, wearing a light pink wool sweater, walking in from the door.

Luckily.

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

"Nothing."

Chang Haonan replied calmly:

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

"Uh... that's right."

As expected, Yao Mengna didn't understand, and was easily evaded.

Moreover, she took the initiative to change the topic afterwards:

"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 hanging 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 before, and everyone had a lunch box together.

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

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

"Professor Chang?"

Yao Mengna looked at Chang Haonan, who suddenly had a trance, and called out tentatively.

"Oh..."

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

It should take some time to get the result.

"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.