2022/10/14 by Andrés Galindo-Olarte, Juntao Huang, Galindo-Olarte, Andrés +5 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Superconducting Materials and Applications
paper · pdf · doi:10.48550/arxiv.2210.07908
openalex publication_date 2022/10/14 · openalex created_date 2022/10/19 · openalex updated_date 2026/07/28
This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and stability properties. However, to resolve the high dimensional probability distribution function, the computational cost is the main bottleneck even for modern-day supercomputers. This work studies the applicability of a post-processing technique to the DG solution to enhance its accuracy and resolution for the VM system. In particular, we prove the superconvergence of order (2k+(1)/(2)) in the negative order norm for the probability distribution function and the electromagnetic fields when piecewise polynomial degree k is used. Numerical tests including Landau damping, two-stream instability and streaming Weibel instabilities are considered showing the performance of the post-processor.