Online seminar

On January 15, 2020, at 14.00 the first meeting of the online seminar will be held

Seminar Leaders:

1. Principal Researcher of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the RAS professor, corresponding member of RAS, S.I. Kabanikhin.

2. The first vice-rector of Abai KazNPU, Professor M.A. Bektemesov.

3. Dean of the Faculty of Mechanics and Mathematics, Al-Farabi KazNU, PhD Dr. D.B. Zhakebaev.

Novosibirsk, 1, Pirogova, NSU, auditorium 4109

Almaty, 71 al-Farabi Ave., audience 213

Almaty, 13 Dostyk Ave., KazNPU, room 303

TOPIC: «Toward Making Deterministic Solution of the Boltzmann Equation Practical».

Annotation. It is believed that the Boltzmann kinetic equation provides the most accurate description of a gas on a microscopic scale and provides a theoretical basis for gas models on a macroscopic scale. Many recent applications of miniature aerospace technologies represent processes that cover a range of scales from macroscopic to microscopic. For such applications, the Boltzmann equation gives a single description. The development of methods for numerically solving the Boltzmann equation for complex geometries and in several dimensions can help us understand the fundamental processes in noncontinental gases, from flows in small channels to high-speed high-altitude turbulence. At the same time, an effective high-precision solution of the Boltzmann equation turned out to be difficult to achieve. The difficulties lie in the high dimensionality of the equation, the exorbitant cost of estimating the collision operator describing the interaction of molecules, and the significant lack of effective surrogate models to ensure an accurate physical representation in strong non-continuum modes. However, in recent years, engineering and mathematical communities have made significant progress in understanding this problem.

In this presentation, we will discuss several approaches to developing an effective deterministic solution of the Boltzmann equation, including Fourier spectral methods and methods based on Galerkin discontinuous discretizations. We will also try to touch on new ideas for deriving low-order models for noncontinuous data-based gases. Although the subject is quite extensive and technical, every effort will be made to limit the discussion to basic ideas and make the conversation acceptable to undergraduate and graduate students.

SPEAKER:

Alex Alekseenko, Department of Mathematics, California State University, USA.

Teachers, doctoral students, undergraduates, students and comers are invited.