Research field: Numerical methods for kinetic equations in rarefied gas dynamics and plasma physics, and mathematical modeling using differential equations.
Professor: Seung Yeon Cho
Rearch description:
My primary research focus lies in advancing numerical techniques for the Boltzmann equation within the context of rarefied gas dynamics. This equation, originally formulated by Ludwig Boltzmann in 1872, plays a pivotal role in understanding how gas molecules evolve from non-equilibrium to equilibrium states. It provides valuable insights into fundamental properties such as conservation laws and the Second law of Thermodynamics. The applications of the Boltzmann equation span diverse fields, including spacecraft reentry dynamics and the optimization of aircraft airfoil designs.
Despite its significance, developing a numerical method for the Boltzmann equation presents considerable challenges due to the following structural complexities:
(1) high dimensionality of the equation (three dimension both in space and velocity and one dimension in time);
(2) five-fold integral of the collision opertaor;
(3) conservation laws of mass, momentum, energy;
(4) the Second law of Thermodynamics;
(5) the requirement for a positive solution
(6) time step restrictions coming from convection and the Boltzmann collision operator.
As related topics, I have been working on the development of numerical methods for the Boltzmann equation, BGK-type models for mixtures of gases or polyatomic gases, or Vlasov-type models for ion and electrons, and relevant stability and convergence analysis.
Moreover, I am intrigued by recent extensions of kinetic theory, especially how it can model phenomena observed in nature and human society. In this context, I have a deep research interest in modeling human behaviors within financial markets and fashion trend.