# The equilibrium-diffusion limit for radiation hydrodynamics [CL]

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. We derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy. Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). While analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting ${\cal O}(\beta^2)$ terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.

J. Ferguson, J. Morel and R. Lowrie
Fri, 24 Feb 17
49/50

Comments: 16 pages, 1 figure, submitted for publication to the Journal of Quantitative Spectroscopy and Radiative Transfer

# SHARP: A Spatially Higher-order, Relativistic Particle-in-Cell Code [CL]

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher order accurate relativistic PIC algorithm in one spatial dimension which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher order interpolation functions to achieve a spatially higher order accurate algorithm (up to 5th order). We validate our algorithm against several test problems — thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutions of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.

M. Shalaby, A. Broderick, P. Chang, et. al.
Fri, 17 Feb 17
28/43

Comments: 25 pages, 18 figures, submitted to ApJ

# Factorized Runge-Kutta-Chebyshev Methods [CL]

The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) class of explicit schemes for the integration of large systems of PDEs with diffusive terms is presented. FRKC2 schemes are straightforward to implement through ordered sequences of forward Euler steps with complex stepsizes, and easily parallelised for large scale problems on distributed architectures.
Preserving 7 digits for accuracy at 16 digit precision, the schemes are theoretically capable of maintaining internal stability at acceleration factors in excess of 6000 with respect to standard explicit Runge-Kutta methods. The stability domains have approximately the same extents as those of RKC schemes, and are a third longer than those of RKL2 schemes. Extension of FRKC methods to fourth-order, by both complex splitting and Butcher composition techniques, is discussed.
A publicly available implementation of the FRKC2 class of schemes may be obtained from maths.dit.ie/frkc

S. OSullivan
Thu, 16 Feb 17
11/45

Comments: 9 pages, 6 figures, accepted to the proceedings of Astronum 2016 – 11th Annual International Conference on Numerical Modeling of Space Plasma Flows, June 6-10, 2016

# Numerical aspects of Giant Impact simulations [EPA]

In this paper we present solutions to three short comings of Smoothed Particles Hydrodynamics (SPH) encountered in previous work when applying it to Giant Impacts. First we introduce a novel method to obtain accurate SPH representations of a planet’s equilibrium initial conditions based on equal area tessellations of the sphere. This allows one to imprint an arbitrary density and internal energy profile with very low noise which substantially reduces computation because these models require no relaxation prior to use. As a consequence one can significantly increase the resolution and more flexibly change the initial bodies to explore larger parts of the impact parameter space in simulations. The second issue addressed is the proper treatment of the matter/vacuum boundary at a planet’s surface with a modified SPH density estimator that properly calculates the density stabilizing the models and avoiding an artificially low density atmosphere prior to impact. Further we present a novel SPH scheme that simultaneously conserves both energy and entropy for an arbitrary equation of state. This prevents loss of entropy during the simulation and further assures that the material does not evolve into unphysical states. Application of these modifications to impact simulations for different resolutions up to $6.4 \cdot 10^6$ particles show a general agreement with prior result. However, we observe resolution dependent differences in the evolution and composition of post collision ejecta. This strongly suggests that the use of more sophisticated equations of state also demands a large number of particles in such simulations.

Tue, 31 Jan 17
22/58

# Unifying the micro and macro properties of AGN feeding and feedback [HEAP]

We unify the feeding and feedback of supermassive black holes with the global properties of galaxies, groups, and clusters, by linking for the first time the physical mechanical efficiency at the horizon and Mpc scale. The macro hot halo is tightly constrained by the absence of overheating and overcooling as probed by X-ray data and hydrodynamic simulations ($\varepsilon_{\rm BH} \simeq$ 10$^{-3}\,T_{\rm x,7.4}$). The micro flow is shaped by general relativistic effects tracked by state-of-the-art GR-RMHD simulations ($\varepsilon_\bullet \simeq$ 0.03). The SMBH properties are tied to the X-ray halo temperature $T_{\rm x}$, or related cosmic scaling relation (as $L_{\rm x}$). The model is minimally based on first principles, as conservation of energy and mass recycling. The inflow occurs via chaotic cold accretion (CCA), the rain of cold clouds condensing out of the quenched cooling flow and recurrently funneled via inelastic collisions. Within 100 gravitational radii, the accretion energy is transformed into ultrafast 10$^4$ km s$^{-1}$ outflows (UFOs) ejecting most of the inflowing mass. At larger radii the energy-driven outflow entrains progressively more mass: at kpc scale, the velocities of the hot/warm/cold outflows are a few 10$^3$, 1000, 500 km s$^{-1}$, with median mass rates ~10, 100, several 100 M$_\odot$ yr$^{-1}$, respectively. The unified CCA model is consistent with the observations of nuclear UFOs, and ionized, neutral, and molecular macro outflows. We provide step-by-step implementation for subgrid simulations, (semi)analytic works, or observational interpretations which require self-regulated AGN feedback at coarse scales, avoiding the a-posteriori fine-tuning of efficiencies.

Thu, 26 Jan 17
37/68

# Kinetic and radiative power from optically thin accretion flows [HEAP]

We perform a set of general relativistic, radiative, magneto-hydrodynamical simulations (GR-RMHD) to study the transition from radiatively inefficient to efficient state of accretion on a non-rotating black hole. We study ion to electron temperature ratios ranging from $T_{\rm i}/T_{\rm e}=$ 10 to 100, and simulate flows corresponding to accretion rates as low as 10$^{-6}\,\dot M_{\rm Edd}$, and as high as 10$^{-2}\,\dot M_{\rm Edd}$. We have found that the radiative output of accretion flows increases with accretion rate, and that the transition occurs earlier for hotter electrons (lower $T_{\rm i}/T_{\rm e}$ ratio). At the same time, the mechanical efficiency hardly changes and accounts to $\approx$ 3% of the accreted rest mass energy flux, even at the highest simulated accretion rates. This is particularly important for the mechanical AGN feedback regulating massive galaxies, groups, and clusters. Comparison with recent observations of radiative and mechanical AGN luminosities suggests that the ion to electron temperature ratio in the inner, collisionless accretion flow should fall within 10 $<T_{\rm i}/T_{\rm e}<$ 30, i.e., the electron temperature should be several percent of the ion temperature.

Thu, 26 Jan 17
56/68

Comments: 7 pages, 3 figures; submitted to MNRAS | feedback is welcome

# PATCHWORK: A Multipatch Infrastructure for Multiphysics/Multiscale/Multiframe Fluid Simulations [IMA]

We present a “multipatch” infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element is a sophisticated client-router-server framework for efficiently linking processors supporting different regions (“patches”) that must exchange boundary data. This infrastructure may be used with a wide variety of fluid dynamics codes; the only requirement is that their primary dependent variables be the same in all patches, e.g., fluid mass density, internal energy density, and velocity. Its structure can accommodate either Newtonian or relativistic dynamics. The overhead imposed by this system is both problem- and computer cluster architecture-dependent. Compared to a conventional simulation using the same number of cells and processors, the increase in runtime can be anywhere from negligible to a factor of a few; however, one of the infrastructure’s advantages is that it can lead to a very large reduction in the total number of zone-updates.

H. Shiokawa, R. Cheng, S. Noble, et. al.
Mon, 23 Jan 17
25/55

Comments: 17 pages, 9 figures, submitted to ApJ

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