Discontinuous Galerkin algorithms for fully kinetic plasmas

  title={Discontinuous Galerkin algorithms for fully kinetic plasmas},
  author={James Juno and Ammar H. Hakim and Jason M. TenBarge and E. L. Shi and William Dorland},
  journal={J. Comput. Phys.},

Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space

Spectral (transform) methods for solution of Vlasov-Maxwell system have shown significant promise as numerical methods capable of efficiently treating fluid-kinetic coupling in magnetized plasmas. We

Alias-Free, Matrix-Free, and Quadrature-Free Discontinuous Galerkin Algorithms for (Plasma) Kinetic Equations

  • A. HakimJ. Juno
  • Computer Science
    SC20: International Conference for High Performance Computing, Networking, Storage and Analysis
  • 2020
This paper presents a novel version of the discontinuous Galerkin (DG) algorithm, which uses a continuum scheme in which it directly discretize the 6D phase-space using discontinuous basis functions.

Discontinuous Galerkin schemes for a class of Hamiltonian evolution equations with applications to plasma fluid and kinetic problems

In this paper we present energy-conserving, mixed discontinuous Galerkin (DG) and continuous Galerkin (CG) schemes for the solution of a broad class of physical systems described by Hamiltonian

A Deep Dive into the Distribution Function: Understanding Phase Space Dynamics with Continuum Vlasov-Maxwell Simulations

  • J. Juno
  • Physics, Computer Science
  • 2020
A new algorithm for the discretization of VM-FP system of equations for the study of plasmas in the kinetic regime is presented and it is demonstrated how the high fidelity representation of the distribution function permits detailed analysis of the energization mechanisms in fundamental plasma processes such as collisionless shocks.

Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators

We present a novel discontinuous Galerkin algorithm for the solution of a class of Fokker-Planck collision operators. These operators arise in many fields of physics, and our particular application

Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods

We present an energy-conserving discontinuous Galerkin scheme for the full-$f$ electromagnetic gyrokinetic system in the long-wavelength limit. We use the symplectic formulation and solve directly



Discontinuous Galerkin Methods for the Vlasov-Maxwell Equations

It is proven, up to some boundary effects, that charge is conserved and the total energy can be preserved with suitable choices of the numerical flux for the Maxwell equations and the underlying approximation spaces.

Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system

A brief survey of the discontinuous Galerkin method for the Boltzmann-Poisson equations

This paper gives a brief survey of the discontinuous Galerkin (DG) method, which is a finite element method using discontinuous piecewise polynomials as basis functions and numerical fluxes based on upwinding for stability, for solving the Boltzmann-Poisson system.

Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

The theoretical and algorithmic aspects of the Runge–Kutta discontinuous Galerkin methods are reviewed and several applications including nonlinear conservation laws, the compressible and incompressible Navier–Stokes equations, and Hamilton–Jacobi-like equations are shown.

The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multi-D systems

The algorithm formulation and practical implementation issues such as the numerical fluxes, quadrature rules, degrees of freedom, and the slope limiters are discussed, both in the triangular and the rectangular element cases.

A Unified Gas Kinetic Scheme for Continuum and Rarefied Flows V: Multiscale and Multi-Component Plasma Transport

As a continuation of developing multiscale method for the transport phenomena, a unified gas kinetic scheme (UGKS) for multi-scale and multi-component plasma simulation is constructed. The current

SpectralPlasmaSolver: a Spectral Code for Multiscale Simulations of Collisionless, Magnetized Plasmas

An assessment of the performance of the code is presented, showing a significant improvement in the code running-time achieved by preconditioning, while strong scaling tests show a factor of 10 speed-up using 16 threads.

Continuum Kinetic and Multi-Fluid Simulations of Classical Sheaths

The kinetic study of plasma sheaths is critical, among other things, to understand the deposition of heat on walls, the effect of sputtering, and contamination of the plasma with detrimental