A simple unsplit Godunov method for multidimensional MHD

By James M. Stone, Thomas A. Gardiner. 2009

158 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/ef03d092fa4e715a545a65ab86b70cd739b1bd9c

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In Applied Mathematics

In Astronomy and Astrophysics

In Computational Mechanics

Citations in the corpus

Three-phase Interstellar Medium in Galaxies Resolving Evolution with Star Formation and Supernova Feedback (TIGRESS): Algorithms, Fiducial Model, and Convergence (2016, methodology): “In this paper, we use Athenaʼs predictor-corrector type integrator (Stone & Gardiner 2009), adopting piecewise linear spatial reconstruction, and employing Roe’s Riemann solver.”
Modeling UV Radiation Feedback from Massive Stars. II. Dispersal of Star-forming Giant Molecular Clouds by Photoionization and Radiation Pressure (2018, methodology): “In Paper I we described our implementation and tests of adaptive ray tracing in the Athena magnetohydrodynamics code (Stone & Gardiner 2009), for which we adopted the novel parallelization algorithm proposed by Rosen et al. (2017) as well as several other improvements.”
THREE-DIMENSIONAL SOLAR WIND MODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID (2010, methodology): “…transport (CT) or CT/central difference (CD) approach (Evans & Hawley 1988; Balsara & Spicer 1999; Tóth 2000; Ziegler 2005; Londrillo & Del Zanna 2004; Stone & Gardiner 2009; Li 2008; Cunningham et al. 2009; Lee & Deane 2009), the reconstruction method (Balsara & Kim 2004; Londrillo & Del Zanna…”
THREE-DIMENSIONAL HYDRODYNAMIC SIMULATIONS OF MULTIPHASE GALACTIC DISKS WITH STAR FORMATION FEEDBACK. I. REGULATION OF STAR FORMATION RATES (2013, methodology): “We utilize the Athena code with the van Leer integrator (Stone & Gardiner 2009), Roe’s Riemann solver, a piecewise linear spatial reconstruction scheme, and the orbital advection method for a shearing box (Stone & Gardiner 2010).”
The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers (2020, methodology): “Subsequently, the code was augmented with different time integrators (Stone & Gardiner 2009), the shearing-box approximation (Stone & Gardiner 2010), cylindrical coordinates (Skinner & Ostriker 2010), special relativity (Beckwith & Stone 2011), particles (Bai & Stone 2010a), sink particles (Gong &…”
MOMENTUM INJECTION BY SUPERNOVAE IN THE INTERSTELLAR MEDIUM (2014, methodology): “We solve the hydrodynamics equations with cooling using the Athena code, which employs an unsplit Godunov algorithm (Stone et al. 2008; Stone & Gardiner 2009).”
IMPLEMENTATION OF THE SHEARING BOX APPROXIMATION IN ATHENA (2010, methodology): “The basic MHD algorithms in Athena are documented in Gardiner & Stone (2005a; 2008), and details of the implementation and tests of the methods are given in Stone et al. (2008, hereafter SGTHS) and Stone & Gardiner (2009).”