An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics: a staggered dissipation-control differencing algorithm

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Dedalus: A flexible framework for numerical simulations with spectral methods (2019, background): “The Orszag-Tang vortex problem [97] is a standard compressible magnetohydrodynamics (MHD) test problem in astrophysics (e.g. for the ﬁxed-grid Godunov code Athena [98, 99], the ﬁnite diﬀerence code Flash [100], smoothed-particle hydrodynamic codes [101], moving mesh codes [102], etc.).”
Raining on black holes and massive galaxies: the top-down multiphase condensation model (2016, methodology): “The numerical integrator is the recent third-order accurate unsplit piecewise parabolic method solver (Lee & Deane 2009).”
Chaotic cold accretion on to black holes (2013, methodology): “We use a modified version of the AMR FLASH4 code (Fryxell et al. 2000; Lee & Deane 2009) to integrate the equations of hydrodynamics (see Section 3 and Gaspari et al. 2011a,b for more details).”
THREE-DIMENSIONAL SOLAR WIND MODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID (2010, methodology): “…& 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 2004; Li & Li 2004; Li 2008; Balsara 2009; Balsara et…”