High-order Godunov schemes for global 3D MHD simulations of accretion disks

Flock, Mario; Dzyurkevich, Natalia; Klahr, Hubert; Mignone, A.

doi:10.1051/0004-6361/200912443

Cited by 42 publications

(74 citation statements)

References 58 publications

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“…where The magnetic field is evolved using the constrained transport formalism (see, e.g., the papers by Mignone et al 2007;Flock et al 2010). …”

Section: Standard Nonlinear Stepmentioning

confidence: 99%

“…We test the FARGO-MHD scheme on the linear MRI in global disks, following the setup presented by Flock et al (2010). This test is very sensitive to the numerical consistency and, at the same time, the MRI growth rates are affected by the numerical dissipation of the scheme.…”

Section: Linear Mri In Global Diskmentioning

confidence: 99%

“…As a final application, we consider a turbulent accretion disk in 3D spherical coordinates (r, θ, φ) using the setup BO described by Flock et al (2011). The initial condition consists of a vertically stratified structure in a Newtonian central potential Φ = −1/r with density…”

Section: Turbulent Accretion Diskmentioning

confidence: 99%

“…Representative astrophysical scenarios involve magnetically driven turbulence in accretion disks around compact objects, which are typically modeled via a local approach (the so-called shearing-box model of Hawley et al 1995) or global disk simulations, that have recently become more appealing owing to increases in the available computational power (see, for instance Beckwith et al 2011;Flock et al 2011;Sorathia et al 2012). Likewise, in the context of planet formation, simulations of proto-planetary disks have become an important tool for the study of the dynamics of the gas and its impact on either particles or planets (see Kley et al 2009;Uribe et al 2011, and references therein).…”

Section: Introductionmentioning

confidence: 99%

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A conservative orbital advection scheme for simulations of magnetized shear flows with the PLUTO code

Mignone¹,

Flock

Stute

et al. 2012

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Context. Explicit numerical computations of hypersonic or super-fast differentially rotating disks are subject to the time-step constraint imposed by the Courant condition, according to which waves cannot travel more than a fraction of a cell during a single time-step update. When the bulk orbital velocity largely exceeds any other wave speed (e.g., sound or Alfvén), as computed in the rest frame, the time step is considerably reduced and an unusually large number of steps may be necessary to complete the computation. Aims. We present a robust numerical scheme to overcome the Courant limitation by improving and extending the algorithm previously known as FARGO (fast advection in rotating gaseous objects) to the equations of magnetohydrodynamics (MHD) using a more general formalism. The proposed scheme conserves total angular momentum and energy to machine precision and works in cartesian, cylindrical, or spherical coordinates. The algorithm has been implemented in the next release of the PLUTO code for astrophysical gasdynamics and is suitable for local or global simulations of accretion or proto-planetary disk models. Methods. By decomposing the total velocity into an average azimuthal contribution and a residual term, the algorithm approaches the solution of the MHD equations through two separate steps corresponding to a linear transport operator in the direction of orbital motion and a standard nonlinear solver applied to the MHD equations written in terms of the residual velocity. Since the former step is not subject to any stability restriction, the Courant condition is computed only in terms of the residual velocity, leading to substantially larger time steps. The magnetic field is advanced in time using the constrained transport method in order to fulfill the divergence-free condition. Furthermore, conservation of total energy and angular momentum is enforced at the discrete level by properly expressing the source terms in terms of upwind Godunov fluxes available during the standard solver. Results. Our results show that applications of the proposed orbital-advection scheme to problems of astrophysical relevance provides, at reduced numerical cost, equally accurate and less dissipative results than standard time-marching schemes.

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“…where The magnetic field is evolved using the constrained transport formalism (see, e.g., the papers by Mignone et al 2007;Flock et al 2010). …”

Section: Standard Nonlinear Stepmentioning

confidence: 99%

Section: Linear Mri In Global Diskmentioning

confidence: 99%

Section: Turbulent Accretion Diskmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A conservative orbital advection scheme for simulations of magnetized shear flows with the PLUTO code

Mignone¹,

Flock

Stute

et al. 2012

A&A

Self Cite

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“…Numerical setup follows the second order PLUTO configuration in Flock et al (2010) with the HLLD Riemann solver. We use a locally isothermal global disk model with H/R = 0.05; r:3.6 -6.6 (128 grid cells); θ : ±5 scale heights (160) and φ : 45 o (128).…”

Section: Modelmentioning

confidence: 99%

Long-term stability of the dead-zone in proto-planetary disks

et al. 2010

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Abstract. We present 3D global non-ideal MHD simulations with a self consistent dynamic evolution of ionization fraction of the gas as result of reduced chemical network. We include X-ray ionization from the star as well as cosmic ray ionization. Based on local gas density and temperature in our chemical network, we determine the magnetic resistivity, which is fed back in MHD simulations. Parameters for dust size and abundance are chosen to have accreting layers and a laminar "dead" mid-plane.

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