A Module for Radiation Hydrodynamic Calculations with ZEUS-2D Using Flux-limited Diffusion

By N. J. Turner, James M. Stone. 2001

165 citations recorded by the source corpus.

A module for the ZEUS-2D code is described that may be used to solve the equations of radiation hydrodynamics to order unity in v/c, in the flux-limited diffusion (FLD) approximation. In this approximation, the factor Eddington tensor f, which closes the radiation moment equations, is chosen to be an empirical function of the radiation energy density. This is easier to implement and faster than full-transport techniques, in which f is computed by solving the transfer equation. However, FLD is less accurate when the flux has a component perpendicular to the gradient in radiation energy density and in optically thin regions when the radiation field depends strongly on angle. The material component of the fluid is here assumed to be in local thermodynamic equilibrium. The energy equations are operator split, with transport terms, radiation diffusion term, and other source terms evolved separately. Transport terms are applied using the same consistent transport algorithm as in ZEUS-2D. The radiation diffusion term is updated using an alternating direction-implicit method with convergence checking. Remaining source terms are advanced together implicitly using numerical root finding. However, when absorption opacity is zero, accuracy is improved by instead treating the compression and expansion source terms using a time-centered differencing scheme. Results are discussed for test problems including radiation-damped linear waves, radiation fronts propagating in optically thin media, subcritical and supercritical radiating shocks, and an optically thick shock in which radiation dominates downstream pressure.

Subfields: Applied Mathematics, Computational Mechanics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c0c581cba4c21c3309279848c667db51d91ddd2a

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Citations in the corpus

Vertical Structure of Gas Pressure-dominated Accretion Disks with Local Dissipation of Turbulence and Radiative Transport (2005, methodology): “First, instead of the Alternating Direction Implicit (ADI) method used by Turner & Stone (2001) to solve the radiation diffusion equation, we now employ the Gauss-Seidel method accelerated by a full multi-grid method.”
Global Radiation-Magnetohydrodynamic Simulations of Black-Hole Accretion Flow and Outflow: Unified Model of Three States (2009, methodology): “We performed the test of two-dimensional radiation propagation (Turner & Stone 2001), finding that the energy loss is less than 0.005% in 600 steps, from which we estimate the error in the energy conservation not to exceed 0.08% during the photon traveling timescale in our simulations.”
Coronal outflow dominated accretion discs: a new possibility for low-luminosity black holes? (2001, background): “The inclusion of radiation in the MHD codes (Turner & Stone 2001), and a detailed study of the dependence of the solution on the accrtion rate will prove crucial to settle the issue.”
Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUS-MP (2005, methodology): “For the RHD implementation in ZEUS-MP, we follow the latter approach, adopting the expression for f given by equation (13) in Turner & Stone (2001): f ¼ 1 2 1 fð ÞI þ 1 2 3f 1ð Þn̂n̂; ð13Þ where n̂ ¼ :E/ j :E j, I is the unit tensor, and f is a scalar ‘‘Eddington factor’’ expressed as a function of…”
Athena: A New Code for Astrophysical MHD (2008, methodology): “The key advantage of the method is its simplicity, making it easy to extend with more complex physics (for example, Stone et al. 1992b; Turner & Stone 2001; De Villiers & Hawley 2003; Hayes & Norman 2003).”
HERACLES: a three-dimensional radiation hydrodynamics code (2007, unknown): “Within the limit of large optical thickness, the diffusion approximation can be used (Mihalas & Mihalas 1984; Dai & Woodward 1998; Turner & Stone 2001).”
GLOBAL STRUCTURE OF THREE DISTINCT ACCRETION FLOWS AND OUTFLOWS AROUND BLACK HOLES FROM TWO-DIMENSIONAL RADIATION-MAGNETOHYDRODYNAMIC SIMULATIONS (2011, methodology): “We also performed the tests of gas−radiation interaction, onedimensional and two-dimensional radiation front propagation, and sub- and super-critical shock, and radiation- dominated shock, finding that the results are in good agreement with those Turner & Stone (2001).”
Smoothed particle hydrodynamics with radiative transfer in the flux-limited diffusion approximation (2004, methodology): “Many of the tests were also performed by Turner & Stone (2001) to test their implementation of a FLD module for the ZEUS-2D code.”
Adaptive ray tracing for radiative transfer around point sources (2001, background): “Please note that there is much more literature on the problem of radiative transfer in two dimensions (c.f. Turner and Stone 2001, and references therein).”
Supercritical Accretion Flows around Black Holes: Two-dimensional, Radiation Pressure-dominated Disks with Photon Trapping (2005, methodology): “The method used in this step is basically the same as that described by Turner & Stone (2001).”
Equations and Algorithms for Mixed-frame Flux-limited Diffusion Radiation Hydrodynamics (2006, methodology): “This may be done either at the same time one is iterating to update the flux divergence term ∇ · F (Whitehouse et al. 2005), or in a separate iteration to be done once the iterative solve for the flux divergence update is complete (Turner & Stone 2001; Hayes et al. 2006).”
The thermodynamics of collapsing molecular cloud cores using smoothed particle hydrodynamics with radiative transfer (2005, unknown): “+ 4πκρB − cκρE , (3) ρ D Dt ( e ρ ) = −p∇ · v − 4πκρB + cκρE , (4) ρ c2 D Dt ( F ρ ) = −∇·P− κρ c F (5) (Mihalas & Mihalas 1984; Turner & Stone 2001).”