2007/12/17 by Thomas A. Gardiner, Thomas Gardiner, James M. Stone · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Computational Fluid Dynamics and Aerodynamics #Gas Dynamics and Kinetic Theory #Geometry #Godunov's scheme #Ideal (ethics) #Magnetohydrodynamics #Mathematical analysis #Mathematics #Mechanics #Nuclear reactor physics and engineering #Numerical analysis #Physics #Plasma #astro-ph
paper · pdf · doi:10.1016/j.jcp.2007.12.017
published as J.Comput.Phys.227:4123-4141,2008 · Extended version of the paper accepted for publication in JCP
arxiv created 2007/12/17 · openalex publication_date 2008/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described by Gardiner & Stone (2005) to three dimensions. This algorithm combines the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We describe the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional ``MHD source terms'' and naturally respect the balance implicit in these terms by the \bf∇⋅ B=0 condition. We compare two different forms for the CTU integration algorithm which require either 6- or 12-solutions of the Riemann problem per cell per time-step, and present a detailed description of the 6-solve algorithm. Finally, we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm.