Speaker: Dr. Xiaofeng Cai (蔡晓峰博士)

Time: 12:30-13:30, 28 September 2021 (Tuesday) (Beijing time)

Venue: C404, Lijiao Building, BNU at Zhuhai

Abstract

The semi-Lagrangian (SL) approach is attractive in transport simulations, especially in climate modeling, due to its numerical stability allowing extra-large time-stepping sizes. In this talk, I will present a truly multidimensional high order conservative semi-Lagrangian discontinuous Galerkin method (multi-SLDG) for transport simulations, which consists of the following parts:

Firstly, for high dimensional problems, it is nontrivial to design the schemes that can satisfy properties of allowing extra-large time-stepping size, mass conservation, and high order accuracy simultaneously. A high-order semi-Lagrangian discontinuous Galerkin (SLDG) method that borrows the idea from CSLAM, will be presented, which enjoy many advantages such as allowing for huge time-stepping size, mass conservative, no splitting error, highly accurate, and positivity-preserving.

Secondly, it is still difficult to apply to a high order transport scheme for solving nonlinear problems. The commutator-free Runge-Kutta (RK) exponential integrators (EI) were proposed by Celledoni, et al. (FGCS, 2003). In the nonlinear transport setting, the RKEI can be used to decompose the evolution of the nonlinear transport into a composition of a sequence of linearized dynamics. When we view the linearized dynamics as a linearized transport process, we naturally combine the proposed SLDG method with the RKEI to obtain a nonlinear transport scheme. In particular, the nonlinear transport schemes for various kinetic models are proposed.

Extensive numerical experiments for some benchmarks will be presented to verify the high order accuracy of the proposed schemes in both space and time discretization; and to show their ability in resolving complex solution structures.

About Dr. Cai

Dr. Xiaofeng Cai is an Assistant Professor of the Research Center for Mathematics at Beijing Normal University and the United International College (BNU-HKBU). Before he joined BNU and UIC, he was a postdoctoral fellow at the University of Delaware and the University of Houston, and received his PhD from Xiamen University. He is developing a package of highly efficient high fidelity numerical schemes for transport simulations with applications in plasma physics, numerical weather prediction, etc.