DATE:

Friday, September 13, 2019

TIME:

3:30 PM

LOCATION:

GMCS-314

SPEAKER:

Alexander Alekseenko, Ph.D, Associate Professor, Department of Mathematics, CSU Northridge.

ABSTRACT:

Believed to be most accurate description of gas at the microscopic scale, the kinetic Boltzmann
equation provides theoretical underpinning to models of gas at the macroscopic scale. Many recent
applications of aerospace and miniature technologies introduce processes that span ranges of scales
from macroscopic to microscopic. For such applications, Boltzmann equation provides a unified
description. Development of methods for solving the Boltzmann equation numerically for complex
geometries and in multiple dimensions can help us understand fundamental processes in non-continuum
gases, from flows in small channels to high speed high altitude turbulence. At the same time,
efficient high-fidelity solution of the Boltzmann equation proved out to be difficult to achieve.
The difficulties are the high dimensionality of the equation, the prohibitive costs to evaluate
the collision operator describing interaction of molecules, and considerable lack of efficient
surrogate models to provide accurate physical representation in regimes of strong non-continuum.
However, in recent years engineering and mathematical communities made significant progress toward
understanding this problem. In this talk we will discuss several approaches to develop efficient
deterministic solution of the Boltzmann equation, including the Fourier spectral methods and methods
based on discontinuous Galerkin discretizations. We will also try to touch on new ideas to derive
low order models for non-continuum gases that are data driven. Although the subject is quite large
and technical, all attempts will be made to limit discussion to the main ideas and to keep the talk
admissible to graduate students.

Short Bio: Dr. Alekseenko’s work is in the area of numerical solution of partial differential and integral
equations. He obtained his Ph.D. in Applied Mathematics from Novosibirsk State University in 1999 in inverse
problems of magneto-electrodynamics under supervision of Dr. Kabanikhin. His postdoctoral studies were at
Penn State and Universityof Minnesota in numerical general relativity under supervision of Dr. Arnold.
In 2003 he joined the faculty at California State University Northridge where he currently works on the
development of fast scalable deterministic solutions of the Boltzmann equation. He actively collaborates
with AFRL on solutions of rarefied gas dynamics. In 2011-13 he was an NRC Research Associate at AFRL at
Wright-Patterson AFB and he was AF Summer Fellow at multiple occasions.

HOST:

Gustaaf Jacobs, Aerospace Engineering

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