2011/03/09 by Francesco Miniati, Daniel Martín, Daniel F. Martin
Engineering · Mathematics · Physics and Astronomy · #Adaptive mesh refinement #Algorithm #Applied mathematics #Astrophysics and Star Formation Studies #Computational Fluid Dynamics and Aerodynamics #Computational science #Computer science #Convergence (economics) #Magnetic field #Magnetohydrodynamics #Mathematical analysis #Mathematics #Mechanics #Physics #Piecewise #Robustness (evolution) #Solar and Space Plasma Dynamics #Solenoidal vector field #Vector field #astro-ph.CO #astro-ph.IM #physics.comp-ph
paper · pdf · doi:10.1088/0067-0049/195/1/5
53 pages, 17 figs, under review by ApJS
arxiv created 2011/03/09 · openalex publication_date 2011/06/23 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM . The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock–cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.