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.Comment: 12 pages, 12 figure

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.Comment: 32 pages, 14 figure, submitted to Journal of Computational Physics (Aug 7 2009

A five-wave HLL Riemann solver for relativistic MHD

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.Comment: 15 pages, 19 figures. Accepted for Publication in MNRA

Linear stability analysis of magnetized relativistic jets: the nonrotating case

We perform a linear analysis of the stability of a magnetized relativistic non-rotating cylindrical flow in the aproximation of zero thermal pressure, considering only the m = 1 mode. We find that there are two modes of instability: Kelvin-Helmholtz and current driven. The Kelvin-Helmholtz mode is found at low magnetizations and its growth rate depends very weakly on the pitch parameter. The current driven modes are found at high magnetizations and the value of the growth rate and the wavenumber of the maximum increase as we decrease the pitch parameter. In the relativistic regime the current driven mode is splitted in two branches, the branch at high wavenumbers is characterized by the eigenfunction concentrated in the jet core, the branch at low wavenumbers is instead characterized by the eigenfunction that extends outside the jet velocity shear region.Comment: 22 pages, 13 figures, MNRAS in pres

A Constrained Transport Method for the Solution of the Resistive Relativistic MHD Equations

We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces and are evolved using the constrained transport formalism. Direct application of Stokes' theorem to Faraday's and Ampere's laws ensures that the resulting discretization is divergence-free for the magnetic field and charge-conserving for the electric field. Hydrodynamic variables retain, instead, the usual zone-centred representation commonly adopted in finite-volume schemes. Temporal discretization is based on Runge-Kutta implicit-explicit (IMEX) schemes in order to resolve the temporal scale disparity introduced by the stiff source term in Ampere's law. The implicit step is accomplished by means of an improved and more efficient Newton-Broyden multidimensional root-finding algorithm. The explicit step relies on a multidimensional Riemann solver to compute the line-averaged electric and magnetic fields at zone edges and it employs a one-dimensional Riemann solver at zone interfaces to update zone-centred hydrodynamic quantities. For the latter, we introduce a five-wave solver based on the frozen limit of the relaxation system whereby the solution to the Riemann problem can be decomposed into an outer Maxwell solver and an inner hydrodynamic solver. A number of numerical benchmarks demonstrate that our method is superior in stability and robustness to the more popular charge-conserving divergence cleaning approach where both primary electric and magnetic fields are zone-centered. In addition, the employment of a less diffusive Riemann solver noticeably improves the accuracy of the computations.Comment: 25 pages, 14 figure

Linear and nonlinear evolution of current-carrying highly magnetized jets

We investigate the linear and nonlinear evolution of current-carrying jets in a periodic configuration by means of high resolution three-dimensional numerical simulations. The jets under consideration are strongly magnetized with a variable pitch profile and initially in equilibrium under the action of a force-free magnetic field. The growth of current-driven (CDI) and Kelvin-Helmholtz (KHI) instabilities is quantified using three selected cases corresponding to static, Alfvenic and super-Alfvenic jets. During the early stages, we observe large-scale helical deformations of the jet corresponding to the growth of the initially excited CDI mode. A direct comparison between our simulation results and the analytical growth rates obtained from linear theory reveals good agreement on condition that high-resolution and accurate discretization algorithms are employed. After the initial linear phase, the jet structure is significantly altered and, while slowly-moving jets show increasing helical deformations, larger velocity shear are violently disrupted on a few Alfven crossing time leaving a turbulent flow structure. Overall, kinetic and magnetic energies are quickly dissipated into heat and during the saturated regime the jet momentum is redistributed on a larger surface area with most of the jet mass travelling at smaller velocities. The effectiveness of this process is regulated by the onset of KHI instabilities taking place at the jet/ambient interface and can be held responsible for vigorous jet braking and entrainment.Comment: 14 pages, 11 figure

Mass Accretion Processes in Young Stellar Objects: Role of Intense Flaring Activity

According to the magnetospheric accretion scenario, young low-mass stars are surrounded by circumstellar disks which they interact with through accretion of mass. The accretion builds up the star to its final mass and is also believed to power the mass outflows, which may in turn have a significant role in removing the excess angular momentum from the star-disk system. Although the process of mass accretion is a critical aspect of star formation, some of its mechanisms are still to be fully understood. On the other hand, strong flaring activity is a common feature of young stellar objects (YSOs). In the Sun, such events give rise to perturbations of the interplanetary medium. Similar but more energetic phenomena occur in YSOs and may influence the circumstellar environment. In fact, a recent study has shown that an intense flaring activity close to the disk may strongly perturb the stability of circumstellar disks, thus inducing mass accretion episodes (Orlando et al. 2011). Here we review the main results obtained in the field and the future perspectives.Comment: 4 pages, 2 Figures; accepted for publication on Acta Polytechnica (Proceedings of the Frascati Workshop 2013

On the convergence of Magnetorotational turbulence in stratified isothermal shearing boxes

We consider the problem of convergence in stratified isothermal shearing boxes with zero net magnetic flux. We present results with the highest resolution to-date--up to 200 grid-point per pressure scale height--that show no clear evidence of convergence. Rather, the Maxwell stresses continue to decrease with increasing resolution. We propose some possible scenarios to explain the lack of convergence based on multi-layer dynamo systems.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter

Astrophysical fluid simulations of thermally ideal gases with non-constant adiabatic index: numerical implementation

An Equation of State (\textit{EoS}) closes the set of fluid equations. Although an ideal EoS with a constant \textit{adiabatic index} $\Gamma$ is the preferred choice due to its simplistic implementation, many astrophysical fluid simulations may benefit from a more sophisticated treatment that can account for diverse chemical processes. Here, we first review the basic thermodynamic principles of a gas mixture in terms of its thermal and caloric EoS by including effects like ionization, dissociation as well as temperature dependent degrees of freedom such as molecular vibrations and rotations. The formulation is revisited in the context of plasmas that are either in equilibrium conditions (local thermodynamic- or collisional excitation- equilibria) or described by non-equilibrium chemistry coupled to optically thin radiative cooling. We then present a numerical implementation of thermally ideal gases obeying a more general caloric EoS with non-constant adiabatic index in Godunov-type numerical schemes.We discuss the necessary modifications to the Riemann solver and to the conversion between total energy and pressure (or vice-versa) routinely invoked in Godunov-type schemes. We then present two different approaches for computing the EoS.The first one employs root-finder methods and it is best suited for EoS in analytical form. The second one leans on lookup table and interpolation and results in a more computationally efficient approach although care must be taken to ensure thermodynamic consistency. A number of selected benchmarks demonstrate that the employment of a non-ideal EoS can lead to important differences in the solution when the temperature range is $500-10^4$ K where dissociation and ionization occur. The implementation of selected EoS introduces additional computational costs although using lookup table methods can significantly reduce the overhead by a factor $3\sim 4$.Comment: 17 pages, 10 figures, Accepted for publication in A&