Cosmos Calling: Need a specialist mathematician in the field of numerical solution of stochastic differential equations
Alexander 4110 Shaenko (ex-engineer Dauria Aerospace, now the head of the Mayak crowdsourcing satellite project) and Stepan Tezyunichev are writing open source software to simulate the thermal conditions of the satellites.
The repository is here .
')
Prior to this, Sasha wrote a disser - “Method for solving the problem of radiant heat transfer without a matrix of angular coefficients” ( dissertation , author's abstract ). The code is here . (it's on VB.NET, braking, but it works and there is even documentation)
Space engineers use the Monte Carlo method and it suddenly came to them, apparently, the system of differential equations is stochastic, since some of them are obtained by random tests.
The guys want to write an algorithm that would solve the system of diffures as quickly as possible, and therefore they need the advice of a mathematician-specialist in the field of numerical solution of stochastic differential equations.
The guys decided to solve the main difficulty by constructing a massively parallel algorithm for calculating the radiation path with the Monte-Carlo method of CUDA. Now they want to use for the integration of their system, and it is of a large dimension, about 100 thousand unknowns, and a rigid, suitable method of integration over time. Conventional explicit methods require too small a time step, and implicit ones require to calculate the right-hand side many times, which is resource intensive.
Therefore, it is necessary to find or construct such an integration method that would be suitable for such a combination of requirements and would allow to be considered quickly.
Now in Russia and in the world as a whole there is no open software that would be tailored to the calculation of the heat exchange of satellites. Those commercial, which are, cost tens and hundreds of thousands of dollars and are not available for ordinary people. There are, of course, open codes just for calculating heat transfer, but in order to calculate full-fledged ones for any real satellite, you need to pretty much dance.
You will say that for ordinary people they are not needed, but this is only as long as you do not want to make your own small satellite company. Most of the domestic private space companies do not have money for such software, and many foreign ones do not have either.
And if you are a student who designs his own satellite on a course or diploma project? Trial version for 30 days may not be enough.
And if you want to understand radiant heat transfer? Or use a good implementation of the ray tracing method for other applications?
In a word, there will be many applications and not only space ones.
The idea of THORIUM was born to Shaenko back in 2007 at the IASS conference in Venice and developed in reflections on the automation of calculations of the strength of interceptors for the 787 passenger aircraft in the Moscow branch of Boeing.
" Radioastron "
At that time, Alexander studied at the graduate school of the Astro-Cosmic Center of FIAN. Lebedeva. There, at that time, they finished making the Radioastron space telescope and thought about Millimetron.
" Millimetron "
In the "Millimetron" it was necessary for several years to maintain a large 10-meter mirror at a temperature of about 4 K (-269 C). For this purpose, the mirror is planned to be placed in the shadow of a multilayered umbrella made of a polymer metallized film, which would protect the delicate apparatus from the thermal radiation of the Sun and the Earth. An umbrella called the “heat shield”. Exactly the same is the American rival JWST, the Space Telescope of James Webb.
The real shape of the heat shield is crumpled twenty-meter sheets of film with a small distance between them. This means that in a good way it is necessary to model every more or less large fold in order to understand how heat will be distributed between them. In addition, different layers have a very different temperature - from about +100 C on the layer illuminated by the Sun to -223 C on the layer facing the mirror. With such a variation, the properties of materials changed very much.
The existing calculation codes did not allow for all this to be taken into account, and therefore the THORIUM - Thermooptic radiation iterative universal module was born. It is based on two ideas that emerged at the end of 2007:
These two principles were implemented and the old code on VB.NET and with the new. “Millimetron” was saved, and THORIUM healed with its own life, helping to design thermal management systems (COTR) for small devices. For example, the COTR DX1 and MCA-N, small Dauria apparatuses were designed with its help.
Vidos old THORIUM with Daurievskiy ICA-N
DX1 in THORIUM
From the point of view of mathematics, THORIUM solves a system of differential equations of non-stationary radiation-conductive heat exchange taking into account the variability of the thermophysical and thermo-optical characteristics of materials. These equations look like this:
Where
c i - specific heat capacity of the i-th element; ρ i - its density; V i - the volume of the element; T i is the element temperature; t is time; N i n - the number of elements having a common face with the i-th element; Qn k i - power transmitted from the k-th neighbor of the i-th element by means of thermal conductivity; S i - the area of the i-th element; Qe i is the outgoing radiant flux density of the i-th element; Qr ij is the power transmitted from the j-th element to the i-th element by means of radiation; N is the number of elements in the model; Qr j m is the power of the radiation emitted by the m-th external source and absorbed in the i-th element; M is the number of radiation sources; Qi i p is the heat release from the p-th internal heat source in the i-th element, P is the number of internal heat sources.
The number N can be greater than 10 5 , the properties of the elements and the boundary conditions can vary very dramatically over time, for example, when a device is turned on or when the sun exits the shadow, you need to integrate 10-20 turns, which is about 120,000 seconds.
So the search for a good method of integrating such a system would be very useful both for authors, for cosmonautics, and for engineering in general.
Who is interested - write in the comments or email Alexander - ark4110@gmail.com.
The repository is here .
')
Prior to this, Sasha wrote a disser - “Method for solving the problem of radiant heat transfer without a matrix of angular coefficients” ( dissertation , author's abstract ). The code is here . (it's on VB.NET, braking, but it works and there is even documentation)
Space engineers use the Monte Carlo method and it suddenly came to them, apparently, the system of differential equations is stochastic, since some of them are obtained by random tests.
The guys want to write an algorithm that would solve the system of diffures as quickly as possible, and therefore they need the advice of a mathematician-specialist in the field of numerical solution of stochastic differential equations.
The guys decided to solve the main difficulty by constructing a massively parallel algorithm for calculating the radiation path with the Monte-Carlo method of CUDA. Now they want to use for the integration of their system, and it is of a large dimension, about 100 thousand unknowns, and a rigid, suitable method of integration over time. Conventional explicit methods require too small a time step, and implicit ones require to calculate the right-hand side many times, which is resource intensive.
Therefore, it is necessary to find or construct such an integration method that would be suitable for such a combination of requirements and would allow to be considered quickly.
What is it for
Now in Russia and in the world as a whole there is no open software that would be tailored to the calculation of the heat exchange of satellites. Those commercial, which are, cost tens and hundreds of thousands of dollars and are not available for ordinary people. There are, of course, open codes just for calculating heat transfer, but in order to calculate full-fledged ones for any real satellite, you need to pretty much dance.
You will say that for ordinary people they are not needed, but this is only as long as you do not want to make your own small satellite company. Most of the domestic private space companies do not have money for such software, and many foreign ones do not have either.
And if you are a student who designs his own satellite on a course or diploma project? Trial version for 30 days may not be enough.
And if you want to understand radiant heat transfer? Or use a good implementation of the ray tracing method for other applications?
In a word, there will be many applications and not only space ones.
THORIUM
The idea of THORIUM was born to Shaenko back in 2007 at the IASS conference in Venice and developed in reflections on the automation of calculations of the strength of interceptors for the 787 passenger aircraft in the Moscow branch of Boeing.
" Radioastron "
At that time, Alexander studied at the graduate school of the Astro-Cosmic Center of FIAN. Lebedeva. There, at that time, they finished making the Radioastron space telescope and thought about Millimetron.
" Millimetron "
In the "Millimetron" it was necessary for several years to maintain a large 10-meter mirror at a temperature of about 4 K (-269 C). For this purpose, the mirror is planned to be placed in the shadow of a multilayered umbrella made of a polymer metallized film, which would protect the delicate apparatus from the thermal radiation of the Sun and the Earth. An umbrella called the “heat shield”. Exactly the same is the American rival JWST, the Space Telescope of James Webb.
The real shape of the heat shield is crumpled twenty-meter sheets of film with a small distance between them. This means that in a good way it is necessary to model every more or less large fold in order to understand how heat will be distributed between them. In addition, different layers have a very different temperature - from about +100 C on the layer illuminated by the Sun to -223 C on the layer facing the mirror. With such a variation, the properties of materials changed very much.
The existing calculation codes did not allow for all this to be taken into account, and therefore the THORIUM - Thermooptic radiation iterative universal module was born. It is based on two ideas that emerged at the end of 2007:
- To calculate the course of radiation in three-dimensional graphics, a lot of software and hardware have been developed, and since external heat transfer is radiant in space, it is possible to use the best practices from graphics to calculate heat transfer.
- If you want to calculate complex structures with a large number of elements in the model, then you should not memorize which elements with which the radiation is exchanged with before starting the calculation. It is more profitable to watch this at each step of integration over time.
These two principles were implemented and the old code on VB.NET and with the new. “Millimetron” was saved, and THORIUM healed with its own life, helping to design thermal management systems (COTR) for small devices. For example, the COTR DX1 and MCA-N, small Dauria apparatuses were designed with its help.
Vidos old THORIUM with Daurievskiy ICA-N
DX1 in THORIUM
From the point of view of mathematics, THORIUM solves a system of differential equations of non-stationary radiation-conductive heat exchange taking into account the variability of the thermophysical and thermo-optical characteristics of materials. These equations look like this:
Where
c i - specific heat capacity of the i-th element; ρ i - its density; V i - the volume of the element; T i is the element temperature; t is time; N i n - the number of elements having a common face with the i-th element; Qn k i - power transmitted from the k-th neighbor of the i-th element by means of thermal conductivity; S i - the area of the i-th element; Qe i is the outgoing radiant flux density of the i-th element; Qr ij is the power transmitted from the j-th element to the i-th element by means of radiation; N is the number of elements in the model; Qr j m is the power of the radiation emitted by the m-th external source and absorbed in the i-th element; M is the number of radiation sources; Qi i p is the heat release from the p-th internal heat source in the i-th element, P is the number of internal heat sources.
The number N can be greater than 10 5 , the properties of the elements and the boundary conditions can vary very dramatically over time, for example, when a device is turned on or when the sun exits the shadow, you need to integrate 10-20 turns, which is about 120,000 seconds.
So the search for a good method of integrating such a system would be very useful both for authors, for cosmonautics, and for engineering in general.
Who is interested - write in the comments or email Alexander - ark4110@gmail.com.
Source: https://habr.com/ru/post/317856/
All Articles