A DG Method for the Micro-Macro Formulation of the Vlasov-Poisson-Lenard-Bernstein System

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PDE Seminar
April 8, 2021
1:50PM - 2:50PM
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Add to Calendar 2021-04-08 13:50:00 2021-04-08 14:50:00 A DG Method for the Micro-Macro Formulation of the Vlasov-Poisson-Lenard-Bernstein System Speaker:  Eirik Endeve (Oak Ridge National Lab) Title:  A DG Method for the Micro-Macro Formulation of the Vlasov-Poisson-Lenard-Bernstein System Abstract:  The Vlasov-Poisson-Lenard-Bernstein (VPLB) system can serve as an approximate model to study transport processes in fusion and space plasmas. These systems are often characterized by multiple spatial and temporal scales, depending on the degree of collisionality. On the one hand, when inter-particle collisions are frequent, the plasma can be described quite well by fluid models. On the other hand, when collisions are infrequent, a fully kinetic description is needed to capture non-equilibrium effects. The micro-Macro (mM) formulation decomposes the particle distribution function into fluid and kinetic components, which are evolved with separate equations that couple through upscaling and downscaling terms. One motivation for adopting the mM model is to gain computational efficiency in collision-dominated regimes. However, maintaining structural properties (e.g., particle, momentum, and energy conservation) is challenging. In this talk, we present a numerical method for the mM formulation of the VPLB system. This method is based on the discontinuous Galerkin (DG) method for phase-space discretization and implicit-explicit time stepping. We focus on the design of consistent discretization of the micro and macro components, which is needed in order to recover conservation properties with the mM method. Numerical results, demonstrating conservation properties and accuracy with coarse phase-space resolution, are also presented. URL associated with Seminar https://research.math.osu.edu/pde/ Zoom ID 6146883919 / Password 314159 Zoom info below Department of Mathematics math@osu.edu America/New_York public
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Speaker:  Eirik Endeve (Oak Ridge National Lab)

Title:  A DG Method for the Micro-Macro Formulation of the Vlasov-Poisson-Lenard-Bernstein System

Abstract:  The Vlasov-Poisson-Lenard-Bernstein (VPLB) system can serve as an approximate model to study transport processes in fusion and space plasmas. These systems are often characterized by multiple spatial and temporal scales, depending on the degree of collisionality. On the one hand, when inter-particle collisions are frequent, the plasma can be described quite well by fluid models. On the other hand, when collisions are infrequent, a fully kinetic description is needed to capture non-equilibrium effects. The micro-Macro (mM) formulation decomposes the particle distribution function into fluid and kinetic components, which are evolved with separate equations that couple through upscaling and downscaling terms. One motivation for adopting the mM model is to gain computational efficiency in collision-dominated regimes. However, maintaining structural properties (e.g., particle, momentum, and energy conservation) is challenging. In this talk, we present a numerical method for the mM formulation of the VPLB system. This method is based on the discontinuous Galerkin (DG) method for phase-space discretization and implicit-explicit time stepping. We focus on the design of consistent discretization of the micro and macro components, which is needed in order to recover conservation properties with the mM method. Numerical results, demonstrating conservation properties and accuracy with coarse phase-space resolution, are also presented.

URL associated with Seminar
https://research.math.osu.edu/pde/

Zoom ID 6146883919 / Password 314159

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