Discontinuous Galerkin algorithms for fully kinetic plasmas

• Published in: Journal of computational physics Vol. 353; pp. 110 - 147
• Main Authors: Juno, J., Hakim, A., TenBarge, J., Shi, E., Dorland, W.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15-01-2018; Elsevier Science Ltd
• Subjects: Algorithms; Computational physics; Computer simulation; Discontinuous Galerkin; Discretization; Distribution functions; Double stars; Finite element method; Fusion; Galerkin method; Kinetics; Numerical methods; Particle accelerators; Plasma; Plasmas (physics); Runge-Kutta method; Vlasov–Maxwell; Vlasov–Maxwell; Discontinuous Galerkin
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2017.10.009

•The discretization of the Vlasov–Maxwell system is high order accurate.•The spatial discretization conserves energy exactly.•The algorithm scales well on distributed memory clusters.•The algorithm permits noise free calculations of the distribution function.•The algorithm has been tested on a five dimensional turbulence calculation.
We present a new algorithm for the discretization of the non-relativistic Vlasov–Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge–Kutta method. Since the Vlasov equation in the Vlasov–Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.