Supercomputing and Computation

High order Semi-Lagrangian Methods for Transport Problems with Applications to Vlasov Simulations and Global Transport

10:00 AM - 11:00 AM
Wei Guo, The University of Houston, Texas
Computer Science and Mathematics Division Seminar Joint Institute for Computational Sciences (Building 5100), Auditorium (Room 128)

Email: Clayton Webster

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. This is joint work with Andrew Christlieb, Maureen Morton, Ram Nair and Jing-Mei Qiu.


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