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Graduate Student Seminar - 12/11/2015

"Towards a Continuum Vlasov-Maxwell Model: Algorithm Developments and Basic Benchmarks"

by James Juno

Friday, December 11, 2015 -- 12:00 p.m.
Large Conference Room, 1207 Energy Research Facility

Advisor:  Professor William Dorland

Two of the most common approaches in computational physics for modeling a physical system are treating the physics in a Lagrangian framework and in an Eulerian, or continuum, framework. Within plasma physics, the Lagrangian framework has been best exemplified by the success of the particle-in-cell (PIC) and hybrid particle-in-cell frameworks. The Eulerian framework, on the other hand, is the host of a diverse array of numerical methods, from finite difference to finite element methods. In the context of a kinetic plasma description, the PIC algorithm has often been favored over the continuum framework because solving a kinetic equation by direct discretization involves simulating a higher dimensional, usually 5D or 6D, phase space solution. Nonetheless, as computational power has increased and algorithms have become more sophisticated, modeling a plasma kinetically by discretization has grown increasingly appealing because of the rich physics in velocity space minimally explored due to the intrinsic noise in the PIC algorithm and the possibility of accurately modeling collisions with a Fokker-Planck or reduced collision operator. Here, we present algorithmic developments, namely the implementation of a discontinuous Galerkin finite element method to discretize space and a semi-implicit time-stepping scheme to discretize time while stepping over extremely restrictive time and space scales, and a few simple benchmarks of Landau damping of Alfvén waves as evidence of the efficacy of this approach, with discussion of how our algorithm scales and its competitiveness with the standard PIC algorithm.

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