Chapter 897 It’s time to bring some small shocks to the industry again...
In the email just sent by Mariam Mirzakhani, it was mentioned that "reverse use of humans to prove the Poincaré conjecture ideas”.
But in fact, if I have to say it, the level set method is closer to the reverse manifold learning algorithm.
Of course, this is not actually the case, but it can be summarized in this way.
The manifold learning algorithm processes high-dimensional data into low-dimensional data, making it easier for humans to understand.
The level set method projects low-dimensional data into high-dimensional data to facilitate computer operations.
In the field of numerical computing, this is a "new" algorithm that was only proposed in the late 1980s, but because its application scope includes but is not limited to liquid atomization, evaporation, combustion, surface material calculations, images Recognition... In short, it is almost all-encompassing like manifold learning, so it was quickly promoted to various fields.
Including TORCMultiphysics, several typical level set methods have also been 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 interval.
This is a very troublesome question.
This is especially true in its main application area - two-phase flow calculations.
Because in most cases, the two fluids involved in the two-phase flow problem can be regarded as mutually immiscible, which means that the method used must effectively maintain the mass of each phase. Conservation.
Therefore, the current level set algorithm is prone to violent oscillation and even divergence in long-axis time calculations -
This should be the best part of the level set algorithm.
For example, in the previous process of designing the turbofan 10 engine combustion chamber, Chang Haonan combined the fluid volume method and the level set method to calculate the dispersion behavior of aviation fuel after leaving the atomization nozzle.
The result...
Useful, but not much.
Compared to the relatively "simple" single-phase fluid calculations in the compressor and turbine parts, the project team received the least guidance during the design process of the combustion chamber and was forced to adopt the old method of combining a lot of experience with pilot testing. .
This also results in more than 60% of the time and money spent on component-level testing.
Fortunately, thanks to the limited volume of the small bypass ratio aviation engine combustion chamber itself, the duration of the diffusion process is not particularly long, so the calculation results will not oscillate too outrageously, and the turbofan The performance indicators pursued by the 10 are really low compared to its superior overall design, so it didn't affect anything in the end.
But if we pursue larger models with more advanced data in the future, behemoths like the GE9X.
Or another application scenario, rocket engine -
Whether it is liquid fuel or solid fuel, since the rocket engine has to carry all its own propellant, it is highly dependent on the combustion-injection process. Far more than 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 to both the symptoms and the symptoms.
Only applicable in certain specific application scenarios.
However, even so, it is a huge improvement for the current level set method.
[…This article will propose a conservation level set method to deal with two-phase flow problems with divergent free velocity fields, and in the process develop efficient processing of Robin boundary conditions on irregular interfaces method, combined with the phase change solution method of interface analysis to consider the influence of liquid shape and internal circulation on heat and mass transfer...]
[First assume an arbitrary region Ω, and its sub-regions Ω1 and Ω2, and There is 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 quickly changes from 1 to 0, and in the sub-region Ω1 , then there is Φ≈1, and in the sub-region Ω2, there is Φ≈0, so Γ is generally set to the 0.5 level set of Φ. In the calculation, we hope that the shape of the interface can be maintained even in the presence of small disturbances... …]
[…]
Time passed quickly as Chang Haonan's hands were tapping rapidly on the keyboard.
But after about twenty minutes, Chang Haonan stopped typing.
After thinking for a while, he pulled out a floppy disk, copied the document he had just written into it, then got up and went straight to the computer room.
In fact, the method he developed is not mathematically complex. It is essentially a re-initialization process that repairs the ψ value in the level set equation by solving a stable solution of a viscous term to achieve the purpose of maintaining conservation.
The reason why no one has ever touched upon it in the past is because it is difficult to implement in terms of specific calculation methods.
For example, the traditional meshing method is difficult to adapt to the high-speed changing two-phase fluid on the Cartesian grid.
But for Chang Haonan, who was the first to specialize in numerical calculations after his rebirth, and also led the development of TORCH Multiphysics software and algorithm design, this was not a problem.
According to his estimation, after the introduction of the finite element discretization method with adaptive grid, the calculation efficiency can still be basically guaranteed.
If you want to operate through non-independent programming, but a simple form of graphical interface interaction, then you probably have to wait until the next major version update of TORCH Multiphysics...
But that’s it. ……
"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 3 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 cannot be hidden no matter what.
Even if Chang Haonan created three versions with different thresholds, at most it would only delay the process to a certain extent.
After all, there are thousands of people who have access to the professional upgraded version of the software. Once the base is large, it is expected that the news will leak out.
Furthermore, after all, competing products are not just for free.
In short, starting around 2000, software such as Materials Studio, ANSYS Fluent, and COMSOL Multiphysics also began to catch up in terms of computing efficiency and performance. Although there is still a distance from the forerunner TORCH Multiphysics in terms of overall performance, they are good at each. In the field, they already have the qualifications to compete.
Although the latter still firmly occupies the top spot in market share thanks to its wide casting net in the past few years and the numerical calculation services provided by Torch Group, its advantages will definitely increase in the long run. The smaller.
Therefore, the work plan submitted by Torch Group in February included a new major version update expected to be launched at the end of 2001 or early 2002.
It is just right to introduce the Cartesian grid 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 and looked at the screen. Calculation process, he said 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 that his blood ran cold.
It has been five years since he was reborn, and he has only been accidentally fooled once, and in the end he was caught red-handed.
Don’t ask, asking means that a man will remain a boy until he dies.
Chang Haonan tried his best to suppress his serious expression and then turned around.
I saw Yao Mengna walking in from the door wearing a light pink woolen sweater.
fine.
From this distance, she should have only heard a few fragments of words.
"Nothing."
Chang Haonan replied calmly:
"I mean, you can't be afraid just because the research direction is difficult."
"Uh...that's true."
Yao Mengna really didn't know 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 you were nowhere to be seen in the office, so I guessed you were in the computer room.”
"Hang the lunch box on the doorknob of your office. Don't forget to eat after you're done."
This situation suddenly reminded Chang Haonan of the first time he saw Yao Mengna after he was reborn.
In the old computer room, there was also a session where everyone had lunch together.
It’s just that Zhang Man seemed to have bought the lunch box at that time...
For a moment, Chang Haonan couldn’t help but fall into memories.
“Professor Chang?”
Yao Mengna looked at Chang Haonan, who was suddenly distracted, and gave a tentative cry.
"Oh..."
Chang Haonan woke up suddenly, and then glanced at the computer that was calculating.
It should take some time to get the results.
“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.
(End of this chapter)