We use cookies in order to improve the quality and usability of the HSE website. More information about the use of cookies is available here, and the regulations on processing personal data can be found here. By continuing to use the site, you hereby confirm that you have been informed of the use of cookies by the HSE website and agree with our rules for processing personal data. You may disable cookies in your browser settings.

  • A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

HSE Scientist Optimises Solution of Hydrodynamics Problems

HSE Scientist Optimises Solution of Hydrodynamics Problems

© iStock

Supercomputers are no longer required to calculate fluid flows in multiscale problems.

Roman Gaydukov, Associate Professor at the MIEM HSE School of Applied Mathematics, has modelled the fluid flow around a rotating disk with small surface irregularities. His solution allows for predicting fluid flow behaviour without the need for powerful supercomputers. The results have been published in Russian Journal of Mathematical Physics.

Hydrodynamics studies the motion of fluids and their interaction with solid surfaces. This branch of physics makes it possible to understand and predict the behaviour of fluids and gases under various conditions. In particular, the principles of hydrodynamics are used in electrochemistry for calculating the reactions of galvanisation, such as silver molecules adhering to a metal surface, and oxidation, such as patina formation on copper.

These processes use a disk electrode, which is a flat metal plate that rotates in a fluid. To accurately calculate electrochemical reactions, it is essential to understand how the fluid moves around the electrode and what conditions that need to be maintained. To achieve this, scientists must account for numerous variables, while even minor irregularities on the disk surface can greatly influence fluid flow, leading to complex and unexpected effects.

Vortex formation near a disc irregularity
© Gaydukov, R. Double-Deck Structure in a Fluid Flow Induced by a Uniformly Rotating Disk with Small Irregularities: the Nonsymmetric Case. Russ. J. Math. Phys. 31, 209–217 (2024).

 

Earlier studies focused solely on symmetrical irregularities, but a scientist at HSE University examined a more complex case. Roman Gaydukov calculated how fluid flow would change with the presence of asymmetrical irregularities on the rotating disk surface.

To do this, he used the method of multideck structures of boundary layers, making it possible to decompose the three-dimensional problem into a series of two-dimensional ones. This method helps solve complex hydrodynamic problems at high Reynolds numbers, where direct modelling is impossible. Although this method has been known since the late 1960s, a rigorous mathematical formulation was only recently developed by the author of the paper together with Professor Vladimir Danilov. The mathematical algorithm of the method can be integrated into any symbolic computation software.

Roman Gaydukov

'Under real conditions, perfectly smooth surfaces do not exist. We have demonstrated how small irregularities on the disk surface affect fluid flow by creating vortex zones and altering the structure of the boundary layer,' explains Roman Gaydukov. 'Our method allows modelling a problem within a few hours, whereas it could take days or even weeks on a supercomputer. This not only saves time but also reduces the cost of computational resources. The method works effectively for large but finite Reynolds numbers.'

The Reynolds number is a dimensionless quantity that describes the relationship between inertial and viscous forces in fluid flow. A large Reynolds number signifies the dominance of inertial forces, which often results in turbulent (chaotic) flows, while a small Reynolds number indicates the dominance of viscous forces, leading to laminar (ordered) flows.

The developed approach can be used to accurately model fluid motion during chemical reactions, with potentially wide applications in industry.

In the future, the scientist plans to extend his research to more complex systems involving interactions between different phases, such as liquid droplets in an air stream or aerosols. This will enable a deeper understanding of the processes in multicomponent and multiphase systems and help improve existing models.

According to Gaydukov, 'Together with my graduate student Nikita Burov, we plan to investigate how the shape of fluid droplets changes as they move through an air flow and how the droplets, as irregularities—including their potential freezing—affect the flow.'

See also:

AI to Enable Accurate Modelling of Data Storage System Performance

Researchers at the HSE Faculty of Computer Science have developed a new approach to modelling data storage systems based on generative machine learning models. This approach makes it possible to accurately predict the key performance characteristics of such systems under various conditions. Results have been published in the IEEE Access journal.

Researchers Present the Rating of Ideal Life Partner Traits

An international research team surveyed over 10,000 respondents across 43 countries to examine how closely the ideal image of a romantic partner aligns with the actual partners people choose, and how this alignment shapes their romantic satisfaction. Based on the survey, the researchers compiled two ratings—qualities of an ideal life partner and the most valued traits in actual partners. The results have been published in the Journal of Personality and Social Psychology.

Trend-Watching: Radical Innovations in Creative Industries and Artistic Practices

The rapid development of technology, the adaptation of business processes to new economic realities, and changing audience demands require professionals in the creative industries to keep up with current trends and be flexible in their approach to projects. Between April and May 2025, the Institute for Creative Industries Development (ICID) at the HSE Faculty of Creative Industries conducted a trend study within the creative sector.

‘The Fundamental Principle of Scientific Knowledge Is Honesty’

Daria Mazur has wanted to pursue science since she was 13 years old—ever since she discovered in the seventh grade that she was good at physics. In an interview for the HSE Young Scientists project, she spoke about her theoretical research on the electric double layer, speed reading, and the MGMT song ‘Little Dark Age.’

From Neural Networks to Stock Markets: Advancing Computer Science Research at HSE University in Nizhny Novgorod

The International Laboratory of Algorithms and Technologies for Network Analysis (LATNA), established in 2011 at HSE University in Nizhny Novgorod, conducts a wide range of fundamental and applied research, including joint projects with large companies: Sberbank, Yandex, and other leaders of the IT industry. The methods developed by the university's researchers not only enrich science, but also make it possible to improve the work of transport companies and conduct medical and genetic research more successfully. HSE News Service discussed work of the laboratory with its head, Professor Valery Kalyagin.

Children with Autism Process Sounds Differently

For the first time, an international team of researchers—including scientists from the HSE Centre for Language and Brain—combined magnetoencephalography and morphometric analysis in a single experiment to study children with Autism Spectrum Disorder (ASD). The study found that children with autism have more difficulty filtering and processing sounds, particularly in the brain region typically responsible for language comprehension. The study has been published in Cerebral Cortex.

HSE Scientists Discover Method to Convert CO₂ into Fuel Without Expensive Reagents

Researchers at HSE MIEM, in collaboration with Chinese scientists, have developed a catalyst that efficiently converts CO₂ into formic acid. Thanks to carbon coating, it remains stable in acidic environments and functions with minimal potassium, contrary to previous beliefs that high concentrations were necessary. This could lower the cost of CO₂ processing and simplify its industrial application—eg in producing fuel for environmentally friendly transportation. The study has been published in Nature Communications. 

HSE Scientists Reveal How Staying at Alma Mater Can Affect Early-Career Researchers

Many early-career scientists continue their academic careers at the same university where they studied, a practice known as academic inbreeding. A researcher at the HSE Institute of Education analysed the impact of academic inbreeding on publication activity in the natural sciences and mathematics. The study found that the impact is ambiguous and depends on various factors, including the university's geographical location, its financial resources, and the state of the regional academic employment market. A paper with the study findings has been published in Research Policy.

Group and Shuffle: Researchers at HSE University and AIRI Accelerate Neural Network Fine-Tuning

Researchers at HSE University and the AIRI Institute have proposed a method for quickly fine-tuning neural networks. Their approach involves processing data in groups and then optimally shuffling these groups to improve their interactions. The method outperforms alternatives in image generation and analysis, as well as in fine-tuning text models, all while requiring less memory and training time. The results have been presented at the NeurIPS 2024 Conference.

When Thoughts Become Movement: How Brain–Computer Interfaces Are Transforming Medicine and Daily Life

At the dawn of the 21st century, humans are increasingly becoming not just observers, but active participants in the technological revolution. Among the breakthroughs with the potential to change the lives of millions, brain–computer interfaces (BCIs)—systems that connect the brain to external devices—hold a special place. These technologies were the focal point of the spring International School ‘A New Generation of Neurointerfaces,’ which took place at HSE University.