The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes

By G. T'oth. 2000

969 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/53d02d6a0614574b40dc9fb94b944fd73fdaec6e

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In Applied Mathematics

In Astronomy and Astrophysics

In Computational Mechanics

Citations in the corpus

OUTFLOW FEEDBACK REGULATED MASSIVE STAR FORMATION IN PARSEC-SCALE CLUSTER-FORMING CLUMPS (2009, methodology): “There are three classes of method for this purpose: constraint transport (CT; Evans & Hawley 1988), projection method, and hyperbolic clean (see, e.g., Tóth 2000 for a review).”
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project (2019, methodology): “…using HARM-Noble given here used the LF approximate Riemann solver as defined in Gammie et al. (2003), RK2 time integration, the FluxCT method of Tóth (2000), and PPM reconstruction (Colella & Woodward 1984) for the primitive variables at cell faces and the electric fields at cell edges (for…”
The Magnetic Connection between the Convection Zone and Corona in the Quiet Sun (2007, result): “…scheme using a number of standard one-, two-, and three-dimensional advection and shock tests (see, e.g., Brio & Wu 1988; Orszag & Tang 1979; Toth 2000 and references therein), and our results compare favorably with similar tests of other high-order schemes (e.g., Toth 2000; Balbàs & Tadmor 2006).”
“Propeller” Regime of Disk Accretion to Rapidly Rotating Stars (2006, methodology): “This was then used to obtain the poloidal components of the magnetic field (Br , Bθ) in divergence-free form (Toth 2000).”
Launching of conical winds and axial jets from the disc–magnetosphere boundary: axisymmetric and 3D simulations (2009, methodology): “To guarantee the absence of magnetic charge, we calculate at each time-step the φ-component of the vector potential Aφ , which is then used to obtain the poloidal components of the magnetic field (Br, Bθ ) in a divergence-free form (Toth 2000).”
PLUTO: A Numerical Code for Computational Astrophysics (2007, methodology): “Among the variety of monopole control strategies proposed in literature (for a review see To´th 2000), we have implemented (1) the eight wave formulation (Powell 1994; Powell et al. 1999) and (2) the constrained transport (CT) of Balsara & Spicer (1999) and Londrillo & del Zanna (2004).”
Long-term GRMHD simulations of neutron star merger accretion discs: implications for electromagnetic counterparts (2018, methodology): “Enforcement of ∇ · B = 0 is achieved with the constrained transport method of Tóth (2000) that uses a cell-centered representation of the magnetic field.”
An unsplit Godunov method for ideal MHD via constrained transport (2005, methodology): “4 ◦ and δx = δy was recently suggested by T´oth [32] and has been adopted elsewhere [23,9] as well.”
Coupling of a global MHD code and an inner magnetospheric model: Initial results (2004, background): “Enforcing this constraint numerically, particularly in shock-capturing codes, can be done in a number of ways [see Tóth, 2000, and references therein].”
Second-Order-accurate Schemes for Magnetohydrodynamics with Divergence-free Reconstruction (2003, background): “Toth (2000) has reported that a very large and unphysical drop in pressure takes place immediately ahead of the shock, especially in regions where the outer fast shock is propagating obliquely to the mesh.”
An MHD gadget for cosmological simulations (2008, methodology): “Additionally we performed several 2D test cases including theFast Rotortest (Tóth 2000; Londrillo & Del Zanna 2000; Balsara & Spicer 1999), aStrong Blast(Londrillo & Del Zanna 2000; Balsara & Spicer 1999) and theOrzang-Tang Vortex (Orzang & Tang 1979; Dai & Woodward 1994; Picone & Dahlburg 1991; Lo”
THREE-DIMENSIONAL SOLAR WIND MODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID (2010, methodology): “…Lagrange multiplier method (Dedner et al. 2002; Feng et al. 2006; Fragile et al. 2005; Kleimann et al. 2009; Kataoka et al. 2009; Mignone et al. 2010), and the projection method (Brackbill & Baranes 1980; Tóth 2000; Balbás et al. 2004; Balsara & Kim 2004; Crockett et al. 2005; Tóth et al. 2006).”
Three-dimensional simulations of supercritical black hole accretion discs - luminosities, photon trapping and variability (2015, methodology): “The divergence-free criterion is enforced using the flux-constrained scheme of Tóth (2000).”
Magnetized Accretion-Ejection Structures: 2.5-dimensional Magnetohydrodynamic Simulations of Continuous Ideal Jet Launching from Resistive Accretion Disks (2002, background): “The versatile advection code (VAC; see x 3.1) offers several ways to ensure the evolution of the magnetic field to be divergence free (Tóth 2000).”
DIRECT CALCULATION OF THE RADIATIVE EFFICIENCY OF AN ACCRETION DISK AROUND A BLACK HOLE (2008, methodology): “We also use parabolic interpolation in the “Flux-CT” scheme of Tóth (2000) that pre- serves the divergence constraint.”
r-process Nucleosynthesis from Three-dimensional Magnetorotational Core-collapse Supernovae (2017, methodology): “GRMHD is implemented in a finite-volume fashion with WENO5 reconstruction (Reisswig et al. 2013; Tchekhovskoy et al. 2007) and the HLLE Riemann solver (Einfeldt 1988) and constrained transport (Tóth 2000) for maintaining div~B = 0.”