Applied Mathematics Colloquium
Dr. Jingmei Qiu, University of Houston
Wednesday, February 19, 2014 · 12 - 1 PM
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
