Talk by Prof. Vinay Kumar Gupta (IIT Indore)
Posted: Mon Mar 24, 2025 7:09 pm
Dear faculty colleagues and students,
All interested faculty members, research scholars, and students are cordially invited to attend the talk by Prof. Vinay Kumar Gupta (IIT Indore) as per the following schedule:
Title: Mathematical modeling of rarefied gases
Date: March 25, 2025 (Tuesday)
Venue: Room no. 6156
Time: 5.00 PM
Abstract:
The traditional equations of fluid dynamics, namely the Euler equations and the Navier–Stokes–Fourier equations, fail to describe many processes in rarefied gases. Hence, they are inadequate for modeling rarefied gas flows. An alternative way of describing rarefied gas flows is through the Boltzmann equation, which is the fundamental equation in kinetic theory and is capable of describing all types of fluid flows—including rarefied gas flows. Notwithstanding, an analytic solution of the Boltzmann equation is almost implausible to obtain, while its numerical solutions are forbiddingly expensive. Hence, researchers try to derive continuum models from the Boltzmann equation through kinetic theory. These models are expected to perform better than the traditional models of fluid dynamics in describing rarefied gas flows and can be solved—at least—numerically with a significantly less cost than solving the Boltzmann equation. As a matter of fact, the Euler equations and the Navier–Stokes–Fourier equations can also be derived from the Boltzmann equation.
In this talk, some of the basic methods in kinetic theory for deriving mathematical models for rarefied (molecular and granular) gas flows will be presented.
Profile of the Speaker:
Dr. Vinay Kumar Gupta is currently working as an Associate Professor in the Department of Mathematics, Indian Institute of Technology (IIT) Indore, India, since 30 August 2024. He joined IIT Indore as an assistant professor on 01 October 2019. Prior to this, Dr. Gupta was a postdoc on the Commonwealth Rutherford Fellowship at the Mathematics Institute, University of Warwick, United Kingdom, from 26 March 2018 until 28 September 2019. He served the Department of Mathematics, SRM Institute of Science and Technology, Chennai, India as an assistant professor from 01 September 2016 until 19 March 2018. Before this, he was a postdoc at the Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany from 14 January 2016 until 31 August 2016. Dr. Gupta earned his doctoral degree (Dr. rer. Nat.) from the RWTH Aachen University, Germany, in September 2015 under the guidance of Prof. Dr. Manuel Torrilhon with thesis titled “Mathematical modeling of rarefied gas-mixtures” and M.S. (Engineering) degree from Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru, India in 2011 with thesis titled “Kinetic theory and Burnett order constitutive relations for a smooth granular gas”. He also earned M.Sc. (Applied Mathematics) degree from Indian Institute of Technology Roorkee, India in 2007. Dr. Gupta has published 16 articles in international journals, including the Journal of Fluid Mechanics, Proceedings of the Royal Society A, and Physical Review E.
Coordinator - Internal Seminars HoD
Department of Mathematics Department of Mathematics
All interested faculty members, research scholars, and students are cordially invited to attend the talk by Prof. Vinay Kumar Gupta (IIT Indore) as per the following schedule:
Title: Mathematical modeling of rarefied gases
Date: March 25, 2025 (Tuesday)
Venue: Room no. 6156
Time: 5.00 PM
Abstract:
The traditional equations of fluid dynamics, namely the Euler equations and the Navier–Stokes–Fourier equations, fail to describe many processes in rarefied gases. Hence, they are inadequate for modeling rarefied gas flows. An alternative way of describing rarefied gas flows is through the Boltzmann equation, which is the fundamental equation in kinetic theory and is capable of describing all types of fluid flows—including rarefied gas flows. Notwithstanding, an analytic solution of the Boltzmann equation is almost implausible to obtain, while its numerical solutions are forbiddingly expensive. Hence, researchers try to derive continuum models from the Boltzmann equation through kinetic theory. These models are expected to perform better than the traditional models of fluid dynamics in describing rarefied gas flows and can be solved—at least—numerically with a significantly less cost than solving the Boltzmann equation. As a matter of fact, the Euler equations and the Navier–Stokes–Fourier equations can also be derived from the Boltzmann equation.
In this talk, some of the basic methods in kinetic theory for deriving mathematical models for rarefied (molecular and granular) gas flows will be presented.
Profile of the Speaker:
Dr. Vinay Kumar Gupta is currently working as an Associate Professor in the Department of Mathematics, Indian Institute of Technology (IIT) Indore, India, since 30 August 2024. He joined IIT Indore as an assistant professor on 01 October 2019. Prior to this, Dr. Gupta was a postdoc on the Commonwealth Rutherford Fellowship at the Mathematics Institute, University of Warwick, United Kingdom, from 26 March 2018 until 28 September 2019. He served the Department of Mathematics, SRM Institute of Science and Technology, Chennai, India as an assistant professor from 01 September 2016 until 19 March 2018. Before this, he was a postdoc at the Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany from 14 January 2016 until 31 August 2016. Dr. Gupta earned his doctoral degree (Dr. rer. Nat.) from the RWTH Aachen University, Germany, in September 2015 under the guidance of Prof. Dr. Manuel Torrilhon with thesis titled “Mathematical modeling of rarefied gas-mixtures” and M.S. (Engineering) degree from Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru, India in 2011 with thesis titled “Kinetic theory and Burnett order constitutive relations for a smooth granular gas”. He also earned M.Sc. (Applied Mathematics) degree from Indian Institute of Technology Roorkee, India in 2007. Dr. Gupta has published 16 articles in international journals, including the Journal of Fluid Mechanics, Proceedings of the Royal Society A, and Physical Review E.
Coordinator - Internal Seminars HoD
Department of Mathematics Department of Mathematics