2009/11/17 by A. Mignone, P. Tzeferacos, Petros Tzeferacos · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Collocation (remote sensing) #Computational Fluid Dynamics and Aerodynamics #Computer science #Discretization #Divergence (linguistics) #Fluid Dynamics and Turbulent Flows #Godunov's scheme #Induction equation #Magnetic field #Magnetohydrodynamics #Mathematical analysis #Mathematics #Momentum (technical analysis) #Numerical analysis #Physics #Quantum mechanics #Upwind scheme #astro-ph.HE #astro-ph.IM #physics.comp-ph
paper · pdf · doi:10.1016/j.jcp.2009.11.026
published as J.Comput.Phys.229:2117-2138,2010 · 31 Pages, 16 Figures Accepted for publication in Journal of Computational Physics
arxiv created 2009/11/17 · openalex publication_date 2009/11/21 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We assess the validity of a single step Godunov scheme for the solution of the magneto-hydrodynamics equations in more than one dimension. The scheme is second-order accurate and the temporal discretization is based on the dimensionally unsplit Corner Transport Upwind (CTU) method of Colella. The proposed scheme employs a cell-centered representation of the primary fluid variables (including magnetic field) and conserves mass, momentum, magnetic induction and energy. A variant of the scheme, which breaks momentum and energy conservation, is also considered. Divergence errors are transported out of the domain and damped using the mixed hyperbolic/parabolic divergence cleaning technique by Dedner et al. (J. Comput. Phys., 175, 2002). The strength and accuracy of the scheme are verified by a direct comparison with the eight-wave formulation (also employing a cell-centered representation) and with the popular constrained transport method, where magnetic field components retain a staggered collocation inside the computational cell. Results obtained from two- and three-dimensional test problems indicate that the newly proposed scheme is robust, accurate and competitive with recent implementations of the constrained transport method while being considerably easier to implement in existing hydro codes.