G. Bodo

PLUTO: A Numerical Code for Computational Astrophysics

We present a new numerical code, PLUTO, for the solution of hypersonic flows in 1, 2, and 3 spatial dimensions and different systems of coordinates. The code provides a multiphysics, multialgorithm modular environment particularly oriented toward the treatment of astrophysical flows in presence of discontinuities. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. Although a plethora of numerical methods has been successfully developed over the past two decades, the vast majority shares a common discretization recipe, involving three general steps: a piecewise polynomial reconstruction followed by the solution of Riemann problems at zone interfaces and a final evolution stage. We have checked and validated the code against several benchmarks available in literature. Test problems in 1, 2, and 3 dimensions are discussed.

THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS

We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell-center in a dimensionally unsplit fashion using the Corner Transport Upwind (CTU) method. Time stepping relies on a characteristic tracing step where piecewise parabolic method (PPM), weighted essentially non-oscillatory (WENO) or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier (GLM) providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes such as viscosity, resistivity and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.

The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics

We present an extension of the piecewise parabolic method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is second-order accurate and employs characteristic projection operators; spatial interpolation is piecewise parabolic making the scheme third-order accurate in smooth regions of the flow away from discontinuities. The algorithm is written for a general system of orthogonal curvilinear coordinates and can be used for computations in non-Cartesian geometries. A nonlinear iterative Riemann solver based on the two-shock approximation is used in flux calculation. In this approximation, an initial discontinuity decays into a set of discontinuous waves only implying that, in particular, rarefaction waves are treated as flow discontinuities. We also present a new and simple equation of state that approximates the exact result for the relativistic perfect gas with high accuracy. The strength of the new method is demonstrated in a series of numerical tests and more complex simulations in one, two, and three dimensions.

MHD simulations of jet acceleration from Keplerian accretion disks. The effects of disk resistivity

Context: Accretion disks and astrophysical jets are used to model many active astrophysical objects, such as young stars, relativistic stars, and active galactic nuclei. However, existing proposals for how these structures may transfer angular momentum and energy from disks to jets through viscous or magnetic torques do not yet provide a full understanding of the physical mechanisms involved. Thus, global stationary solutions have not explained the stability of these structures; and global numerical simulations that include both the disk and jet physics have so far been limited to relatively short time scales and narrow (and possibly astrophysically unlikely) ranges of viscosity and resistivity parameters that may be crucial to defining the coupling of the inflow-outflow dynamics. Aims: We present self-consistent, time-dependent simulations of supersonic jets launched from magnetized accretion disks, using high-resolution numerical techniques. In particular we study the effects of the disks magnetic resistivity, parametrized through an α-prescription, in determining the properties of the inflow-outflow system. Moreover we analyze under which conditions steady state solutions of the type proposed in the self-similar models of Blandford & Payne can be reached and maintained in a self-consistent nonlinear stage. Methods: We used the resistive MHD FLASH code with adaptive mesh refinement (AMR), allowing us to follow the evolution of the structure on a long enough time scale to reach steady state. A detailed analysis of the initial configuration state is given. Results: We obtain the expected solutions within the axisymmetric (2.5 D) limit. Assuming a magnetic field around equipartition with the thermal pressure of the disk, we show how the characteristics of the disk-jet system, such as the ejection efficiency and the energetics, are affected by the anomalous resistivity acting inside the disk.

An HLLC Riemann solver for relativistic flows — I. Hydrodynamics

We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, robust and positively conservative. The performance of the new solver is evaluated through numerical testing in one and two dimensions.

An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The Harten–Lax–van Leer contact wave (HLLC) solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave. Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the constrained transport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one- and two-dimensional numerical test problems.

High‐resolution 3D relativistic MHD simulations of jets

Relativistic magnetized jets are key elements in active galactic nuclei and in other astrophysical environments. Their structure and evolution involve a complex non-linear physics that can be approached by numerical studies only. Still, owing to a number of challenging computational aspects, only a few numerical investigations have been undertaken so far. In this paper, we present high-resolution three-dimensional numerical simulations of relativistic magnetized jets carrying an initially toroidal magnetic field. The presence of a substantial toroidal component of the field is nowadays commonly invoked and held responsible for the process of jet acceleration and collimation. We find that the typical nose cone structures, commonly observed in axisymmetric two-dimensional simulations, are not produced in the three-dimensional case. Rather, the toroidal field gives rise to strong current-driven kink instabilities leading to jet wiggling. However, it appears to be able to maintain a highly relativistic spine along its full length. By comparing low- and high-resolution simulations, we emphasize the impact of resolution on the jet dynamical properties.

A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics

We present a five-wave Riemann solver for the equations of ideal relativistic magnetohydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for the equations of ideal MHD. The solution to the Riemann problem is approximated by a five wave pattern, comprised of two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a nonlinear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular HLL solver or the recently proposed HLLC schemes.

Aspect Ratio Dependence in Magnetorotational Instability Shearing Box Simulations

Three-dimensional numerical simulations of the magnetorotational instability in the shearing box approximation with a nonzero net flux are presented. By changing the size of the computational domain in the radial direction relative to the vertical box height, we find, in agreement with previous studies, that transport of angular momentum (associated with the so-called “channel solution”) is strongly intermittent and maximized for boxes of unit aspect ratio. On the other hand, in boxes with larger aspect ratio the intermittent behavior disappears and angular momentum transport is inhibited.

Formation of dynamical structures in relativistic jets: the FRI case

Context. Strong observational evidence indicates that all extragal actic jets associated with AGNs move at relativistic speed up to 100 pc - 1 kpc scales from the nucleus. At larger distances, reflecting the Fanaro ff-Riley radio source classification, we observe an abrupt dec eleration in FR-I jets while relativistic motions persist up to Mpc scale in FR -II. Moreover, VLBI observations of some object like B2 1144+35, Mrk501 and M87 show limb brightening of the jet radio emission at the parsec scale. This effect is interpreted kinematically as due to the presence of a d eboosted central spine at high Lorentz factor and of a weakly relativi stic external layer. Aims. In this paper we investigate whether these effects can be interpreted by a breaking of the collimated flow by external medium entrainment favored by sh ear instabilities, namely KelvinHelmholtz instabilities. We examine in details the physical conditions under which significant deceleration of a relativistic flow is produced. Methods. We investigate the phenomenon by means of high-resolution three-dimensional relativistic hydrodynamic simulations using the PLUTO code for computational astrophysics. Results. We find that the parameter of utmost importance in determinin g the instability evolution and the entrainment properties is the ambient/jet density contrast. We show that lighter jets suffer stronger slowing down in the external layer than in the central part and conserve a central spine at high Lorentz factor. Conclusions. Our model is verified by constructing synthetic emission map s from the numerical simulations that compare reasonably well with VLBI observations of the inner part of FR-I sources.