Laboratory of Industrial Mathematics

The Laboratory of Industrial Mathematics (LIM) headed by Professor V.M. Goloviznin was established in the Faculty of Computational Mathematics and Cybernetics (CMC) of Lomonosov Moscow State University in 2011. LIM is a pure research laboratory whose budget is fully formed from the research grants won and the industrial contracts completed. The Laboratory was created in response for a growing need of the leading industrial institutions in Russia, such as Saturn, Aviadvigatel, Gidropress, and OKBM Afrikantov, for solving complex problems of science and engineering that require supercomputing and state-of-the-art computational algorithms. In the area of energy and space, examples of topical engineering problems LIM is involved in, include the numerical simulation of new-generation atomic plants and computational aeroacoustics. Such applications critically depend on massive computations. For LIM based at the Chair of Computational Methods at CMC, such computational resources are available through the use of Lomonosov and Chebyshev Supercomputing Facilities that are flagship supercomputers in Russia. On the other hand, for many years, advanced computational algorithms have been an area of active research in the group of Prof. Goloviznin. This group also has an excellent track record of a successful collaboration with various industrial institutions.

Main Scientific directions

• Adaptation of new supercomputing technologies and their further development for the solution of topical applied problems of RosAtom and RosAviaprom institutions.
• Running specialised computer modelling and simulation, high-qualification and certification courses targeted at the engineers of the leading Russian industry.
• Providing new opportunities for coaching CMC students in the field of mathematical modelling with the use of supercomputing.
• Conducting fundamental research in the field of new-generation computational algorithms for peta and emerging exaflop computers.
• Solution of applied industrial problems with the use of supercomputing technologies.

Examples of topical applications for industrial mathematics

Aeroacoustics Modelling

The problem of aircraft noise reduction has become an increasingly important issue: by 2020 the total number of flights is expected to double and, accordingly, each individual aircraft needs to be made at least twice as quiet in order to keep the environmental noise pollution at least to the present level. This is a hard task which leads to ever stringent international noise regulation laws and often forces the aircraft manufacturers to choose an acoustic optimisation in a trade-off against the aerodynamic performance and fuel efficiency.

Mathematical modelling based on computer simulation can significantly enhance the design process of a new-generation aircraft and potentially replace expensive rig tests. Challenges of aeroacoustic modelling include those present in modelling of high-Reynolds number flows in gas dynamics. In addition to them, a specific feature of aeroacoustic calculations is a great diversity of flow scales – from small hydrodynamic fluctuations to large-scale acoustic waves. As if to make it even more difficult for modelling, the bulk of the unsteady flow typically does not radiate sound, and the acoustic part of the flow is very small in comparison with the bulk of unsteady fluctuations in the flow. One typical example is high-speed turbulent jet flows: the acoustic energy of a turbulent jet that has enough power to provide thrust for a commercial aircraft is less than 0.01 percent of its mechanical energy. Hence, to accurately capture the sound generated by an unsteady flow one needs both advanced mathematical modelling approaches and supercomputing resources.

In the group of Prof. Goloviznin, a new computational algorithm was developed – it is based on the CABARET scheme for solving unsteady compressible flow problems at a high Reynolds number. This algorithm has already been successfully applied for several jet noise problems. The group of Prof. Goloviznin maintains active collaboration links with leading aeronautical centres both in Russia and globally, e.g., the TsAGI Acoustics Division, Keldysh Institute of Applied Mathematics, University of Cambridge Department of Engineering, and School of Engineering and Materials Sciences Queen Mary University of London. In addition to it, the group is also well connected with the leading Russian industry, e.g., Saturn and Aviadvigatel. As for the aeroacoustics research, the Lab invesigates:

• jet noise modelling, including single and dual stream jet calculations in statistic and flight conditions, mathematical modelling of noise suppression concepts;
• modelling of a jet – the airframe interaction for investigation of jet-induced effects on the cabin noise;
• modelling of a jet – the wing-flap interaction for a new generation aircraft with high and ultra-high bypass ratios;
• modelling of the airfoil noise and trailing edge noise.

Thermo-Convection Modelling

Despite the tragic events in Japan that followed a severe accident at the Fukushima atomic plant, nuclear energy remains a major source of energy for economics worldwide without a feasible alternative in the coming years. In Russia, the nuclear engineering also occupies a substantial part of the energy sector and there is a corresponding federal programme entitled “Nuclear energy technologies of new generation for 2010-2015 and through to 2020”. This program is devoted to new emerging technologies in nuclear engineering, and mathematical modelling plays an important role in the development of such technologies.

One of the topical problems in this area is modelling of the heat-mass transfer in large-scale hydraulic systems such as industrial heat exchangers and coolant pipe systems. These flows are dominated by large-scale inertial / convection effects at high Reynolds and Raleigh numbers that appear to be hardly amenable to empirical turbulence models. On the other hand, high-resolution computational methods based on a direct simulation of large-scale turbulent structures, such as Large Scale Simulations (LES) and Coarse-grid Direct Numerical Simulations, are ideally suitable for such complex applications involving a large-scale anisotropic mixing.

In particular, the new computational approach for incompressible flow modelling, the so-called Perfect LES method developed in the group of Prof. Goloviznin at the Chair of Computational Methods and in Moscow Nuclear Safety Institute (IBRAE), is one of the promising approaches in the field. Up to now, the new approach has been validated on a wide range of test problems including a recent T-Junction test that was an international blind test exercise for Computational Fluid Dynamics codes used in thermo-hydraulic calculations for nuclear engineering. At present, the Perfect LES approach has been used for solving applied problems of leading nuclear engineering industry in Russia, such as Gidropress and OKBM Afrikantov, with using Chebyshev and Lomonosov supercomputing facilities. The thermo-convection area of activities of the Laboratory includes the following research directions:

• numerical simulation of temperature fluctuations in pipeline coolant systems at large Raleigh number regimes, modelling of the thermo-stripping effect in application to the thermal fatigue and durability of the pipe work;
• thermo-hydraulic calculations of the active reactor zone and heat exchangers at large Reynolds numbers using the Perfect LES approach.