# Applied Mathematics Colloquium

### Dr. Jingmei Qiu, University of Houston

Location

Mathematics/Psychology : 101

Date & Time

February 19, 2014, 12:00 pm – 1:00 pm

Description

Title: High order Semi-Lagrangian Methods for transport problems with

applications to Vlasov Simulations and Global Transport

Abstract: The semi-Lagrangian (SL) scheme for transport problems gains

more and more popularity in the computational science community due to its

attractive properties. For example, the SL scheme, compared with the

Eulerian approach, allows extra large time step evolution by incorporating

characteristics tracing mechanism, hence achieving great computational

efficiency. In this talk, we will introduce a family of dimensional

splitting high order SL methods coupled with high order finite

difference weighted essentially non-oscillatory (WENO) procedures and

finite element discontinuous Galerkin (DG) methods. By performing

dimensional splitting, the multi-dimensional problem is decoupled into a

sequence of 1-D problems, which are much easier to solve numerically in

the SL setting. The proposed SL schemes are applied to the Vlasov model

arising from the plasma physics and the global transport problems based on

the cubed-sphere geometry from the operational climate model. We further

introduce the integral defer correction (IDC) framework to reduce the

dimensional splitting errors. The proposed algorithms have been

extensively tested and benchmarked with classical problems in plasma

physics such as Landau damping, two stream instability, Kelvin-Helmholtz

instability and global transport problems on the cubed-sphere.

Location: Math/Psych room 101