Prof. Alexander Kurganov
Prof. Alexander Kurganov
Southern University of Science and Technology, China
Title: Central Schemes: A Powerful Black-Box Solver for Nonlinear Hyperbolic PDEs

The talk will be focused on non-oscillatory central schemes, which are simple, efficient, highly accurate and robust Godunov-type finite-volume methods for general hyperbolic systems of conservation laws. I will first show their derivation and then recent applications. 

I will first give a brief description of Godunov-type finite-volume methods for general hyperbolic systems of conservation laws. These methods consist of two types of schemes: upwind and central. My lecture will focus on the second type -- non-oscillatory central schemes. 

Godunov-type schemes are projection-evolution methods. In these methods, the solution, at each time step, is interpolated by a (generically discontinuous) piecewise polynomial interpolant, which is then evolved to the next time level using the integral form of conservation laws. Therefore, in order to design an upwind scheme, (generalized) Riemann problems have to be (approximately) solved at each cell interface. This, however, may be hard or even impossible. 

The main idea in the derivation of central schemes is to avoid solving Riemann problems by averaging over the wave fans generated at cell interfaces. This strategy leads to a family of universal numerical methods that can be applied as a black-box solver to a wide variety of hyperbolic PDEs and related problems. At the same time, central schemes suffer from (relatively) high numerical viscosity, which can be reduced by incorporating of some upwinding information into the scheme derivation -- this leads to central-upwind schemes, which will be presented in the lecture.


Alexander Kurganov did his Bachelor and Masters studies in Mathematics at the Moscow State University graduating in 1989. He earned his PhD degree in Applied Mathematics at Tel Aviv University in 1998. Since then, he has held several academic positions at the Departments of Mathematics at the University of Michigan (Assistant Professor, 1998-2001), Tulane University (Assistant, Associate and Full Professor, 2001-present) and Southern University of Science and Technology of China (Full Professor, 2016-present). 

Alexander Kurganov also had several short-term visiting positions in the USA, France, Germany and China. Alexander Kurganov has written more than 90 research papers, his current citation index is 1354 (according to MathSciNet) and 4783 (according to Google Scholar). He has supervised 11 PhD and 2 M.Sc. graduate students. Alexander Kurganov has been awarded many NSF, ONR and NSFC grants. He has been an editor in several research journals. He has delivered many talks at conferences, colloquia and seminars throughout the world.