2020/05/27 by Maria Han Veiga, Veiga, Maria Han, David A Velasco Romero +5
Engineering · #65Mxx #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #G.1.8 #G.4 #Instrumentation and Methods for Astrophysics (astro-ph.IM) #J.2 #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2005.13563
openalex publication_date 2020/05/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We study in this paper three variants of the high-order Discontinuous\nGalerkin (DG) method with Runge-Kutta (RK) time integration for the induction\nequation, analysing their ability to preserve the divergence free constraint of\nthe magnetic field. To quantify divergence errors, we use a norm based on both\na surface term, measuring global divergence errors, and a volume term,\nmeasuring local divergence errors. This leads us to design a new, arbitrary\nhigh-order numerical scheme for the induction equation in multiple space\ndimensions, based on a modification of the Spectral Difference (SD) method [1]\nwith ADER time integration [2]. It appears as a natural extension of the\nConstrained Transport (CT) method. We show that it preserves\n\∇\⋅\B=0 exactly by construction, both in a local and a global\nsense. We compare our new method to the 3 RKDG variants and show that the\nmagnetic energy evolution and the solution maps of our new SD-ADER scheme are\nqualitatively similar to the RKDG variant with divergence cleaning, but without\nthe need for an additional equation and an extra variable to control the\ndivergence errors.\n [1] Liu Y., Vinokur M., Wang Z.J. (2006) Discontinuous Spectral Difference\nMethod for Conservation Laws on Unstructured Grids. In: Groth C., Zingg D.W.\n(eds) Computational Fluid Dynamics 2004. Springer, Berlin, Heidelberg\n [2] Dumbser M., Castro M., Par 'es C., Toro E.F (2009) ADER schemes on\nunstructured meshes for nonconservative hyperbolic systems: Applications to\ngeophysical flows. In: Computers & Fluids, Volume 38, Issue 9\n