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1.
A third-order shock-capturing numerical scheme for three-dimensional special relativistic magnetohydrodynamics (3-D RMHD) is presented. Due to the difficulties in developing exact or even approximate Riemann solvers in RMHD, a simple two-speed central-type solver that requires the knowledge of only the local fast magnetosonic velocities is employed. First results from axisymmetric simulations of Pulsar Wind Nebulae (PWNe) are finally presented. We show that when the wind magnetization is high enough, magnetic hoop stresses at work downstream of the termination shock are able to collimate a polar jet-like outflow, with velocities similar to those observed in the Crab and Vela Nebulae (v ≈ 0.5-0.7c).  相似文献   

2.
We describe a numerical algorithm based on Godunov methods for integrating the equations of compressible magnetohydrodynamics (MHD) in multidimensions. It combines a simple, dimensionally-unsplit integration method with the constrained transport (CT) discretization of the induction equation to enforce the divergence-free constraint. We present the results of a series of fully three-dimensional tests which indicate the method is second-order accurate for smooth solutions in all MHD wave families, and captures shocks, contact and rotational discontinuities well. However, it is also more diffusive than other more complex unsplit integrators combined with CT. Thus, the primary advantage of the method is its simplicity. It does not require a characteristic tracing step to construct interface values for the Riemann solver, it is straightforward to extend with additional physics, and it is suitable for use with nested and adaptive meshes. The method is implemented as one of two dimensionally unsplit MHD integrators in the Athena code, which is freely available for download from the web.  相似文献   

3.
We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising 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 non-linear 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 Harten–Lax–van Leer solver or the recently proposed HLLC schemes.  相似文献   

4.
A new general relativistic magnetohydrodynamics (GRMHD) code “RAISHIN” used to simulate jet generation by rotating and non-rotating black holes with a geometrically thin Keplarian accretion disk finds that the jet develops a spine-sheath structure in the rotating black hole case. Spine-sheath structure and strong magnetic fields significantly modify the Kelvin-Helmholtz (KH) velocity shear driven instability. The RAISHIN code has been used in its relativistic magnetohydrodynamic (RMHD) configuration to study the effects of strong magnetic fields and weakly relativistic sheath motion, c/2, on the KH instability associated with a relativistic, γ=2.5, jet spine-sheath interaction. In the simulations sound speeds up to and Alfvén wave speeds up to ∼0.56c are considered. Numerical simulation results are compared to theoretical predictions from a new normal mode analysis of the RMHD equations. Increased stability of a weakly magnetized system resulting from c/2 sheath speeds and stabilization of a strongly magnetized system resulting from c/2 sheath speeds is found.  相似文献   

5.
A method is presented for the numerical study of the temporal evolution of nonlinear periodic waves in solar coronal loops which are approximated by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. This method uses a fast Fourier transform technique to calculate spatial derivatives and a modified Euler algorithm for the time scheme for solving cold magnetohydrodynamic equations that govern nonlinear perturbations. The numerical results show that nonlinearity can play a significant role, leading to wave breaking of the kink wave and slab demolition for the sausage one. The kink periodic wave adjusts better to the smoothed slab than the sausage wave.  相似文献   

6.
The system of 1-D ideal MHD equations is numerically solved using the WENO scheme. We then simulated the interplanetary collisionless shock wave and investigated the interaction between the perpendicular collisionless shock wave and two kinds of interplanetary structures, structures with opposite magnetic fields and high-density plasmoids. The results are compared with those of particle simulation: they are found to be very similar. For most phenomena concerned with collisionless shock waves, the ideal MHD simulation is accurate and feasible. Moreover, it has a high computational efficiency and is readily extended to the 2-D or 3-D case.  相似文献   

7.
FLASH is a publicly available astrophysical community code designed to solve highly compressible multi-physics reactive flows. We are adding capabilities to FLASH that will make it an open science code for the academic HEDP community. Among many important numerical requirements, we consider the following features to be important components necessary to meet our goals for FLASH as an HEDP open toolset. First, we are developing computationally efficient time-stepping integration methods that overcome the stiffness that arises in the equations describing a physical problem when there are disparate time scales. To this end, we are adding two different time-stepping schemes to FLASH that relax the time step limit when diffusive effects are present: an explicit super-time-stepping algorithm (Alexiades et al. in Com. Num. Mech. Eng. 12:31–42, 1996) and a Jacobian-Free Newton-Krylov implicit formulation. These two methods will be integrated into a robust, efficient, and high-order accurate Unsplit Staggered Mesh MHD (USM) solver (Lee and Deane in J. Comput. Phys. 227, 2009). Second, we have implemented an anisotropic Spitzer-Braginskii conductivity model to treat thermal heat conduction along magnetic field lines. Finally, we are implementing the Biermann Battery term to account for spontaneous generation of magnetic fields in the presence of non-parallel temperature and density gradients.  相似文献   

8.
A Godunov-type scheme for relativistic magnetohydrodynamic (MHD) equations is developed. We consider the Maxwell equations and dynamic equations for a gas with perfect conductivity in hyperbolic form as was suggested by van Putten. To calculate the fluxes of conservative variables through cells' interfaces we suggest an algorithm for the solution of the linearized Riemann problem. 'Primitive' variables are calculated by solving a non-linear system using the Newton method .  相似文献   

9.
We present a fast solver for computing potential and linear force-free fields (LFFF) above the full solar disk with a synoptic magnetic map as input. The global potential field and the LFFF are dealt with in a unified way by solving a three-dimensional Helmholtz equation in a spherical shell and a two-dimensional Poisson equation on the solar surface. The solver is based on a combination of the spectral method and the finite-difference scheme. In the longitudinal direction the equation is transformed into the Fourier spectral space, and the resulting two-dimensional equations in the r?C?? plane for the Fourier coefficients are solved by finite differencing. The solver shows an extremely fast computing speed, e.g., the computation for a magnetogram with a resolution of 180(??)×360(?) is completed in less than 2 s. Even on a high-resolution 600×1200 grid, the solution can be obtained within only about one minute on a single CPU. The solver can potentially be applied directly to the original resolution of observed magnetograms from SDO/HMI for routinely analyzing daily full-disk data.  相似文献   

10.
We present the results of an exhaustive numerical study of fully relativistic non-axisymmetric Bondi–Hoyle accretion on to a moving Schwarzschild black hole. We have solved the equations of general relativistic hydrodynamics with a high-resolution shock-capturing numerical scheme based on a linearized Riemann solver. The numerical code was previously used to study axisymmetric flow configurations past a Schwarzschild black hole. We have analysed and discussed the flow morphology for a sample of asymptotically high Mach number models. The results of this work reveal that initially asymptotic uniform flows always accrete on to the hole in a stationary way, which closely resembles the previous axisymmetric patterns. This is in contrast with some Newtonian numerical studies where violent flip-flop instabilities were found. As discussed in the text, the reason can be found in the initial conditions used in the relativistic regime, as they cannot exactly duplicate the previous Newtonian setups where the instability appeared. The dependence of the final solution on the inner boundary condition as well as on the grid resolution has also been studied. Finally, we have computed the accretion rates of mass and linear and angular momentum.  相似文献   

11.
G. Jovanović 《Solar physics》2014,289(11):4085-4104
We derive the dispersion equation for gravito-magnetohydrodynamical (MHD) waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. Sound and Alfvén speeds are constant. Under these conditions, it is possible to derive analytically the equations for gravito-MHD waves. The high values of the viscous and magnetic Reynolds numbers in the solar atmosphere imply that the dissipative terms in the MHD equations are negligible, except in layers around the positions where the frequency of the MHD wave equals the local Alfvén or slow wave frequency. Outside these layers the MHD waves are accurately described by the equations of ideal MHD. We consider waves that propagate energy upward in the atmosphere. For the plane boundary, z=0, between two isothermal plasma regions with horizontal but different magnetic fields, we discuss the boundary conditions and derive the equations for the reflection and transmission coefficients. In the simpler case of a gravitationally stratified plasma without magnetic field, these coefficients describe the reflection and transmission properties of gravito-acoustic waves.  相似文献   

12.
We present numerical simulations of the axisymmetric accretion of a massive magnetized plasma torus on a rotating black hole. We use a realistic equation of state, which takes into account neutrino cooling and energy loss due to nucleus dissociations. The calculation are performed in the ideal relativistic MHD approximation using an upwind conservative scheme that is based on a linear Riemann solver and the constrained transport method to evolve the magnetic field. The gravitational attraction of the black hole is introduced via the Kerr metric in the Kerr–Schild coordinates. We simulate various magnetic field configurations and torus models, both optically thick and thin for neutrinos.We have found an effect of alternation of the magnetic field orientation in the ultrarelativistic jet formed as a result of the collapse. The calculations show evidence for heating of the wind surrounding the collapsar by the shock waves generated at the jet–wind border. It is shown that the neutrino cooling does not significantly change either the structure of the accretion flow or the total energy release of the system. The angular momentum of the accreting matter defines the time scale of the accretion. Due to the absence of the magnetic dynamo in our calculations, the initial strength and topology of the magnetic field determines the magnetization of the black hole, jet formation properties and the total energy yield. We estimate the total energy of accretion which transformed to jets as 1.3 × 1052 ergs which was sufficient to explain hypernova explosions like GRB 980425 or GRB 030329.  相似文献   

13.
We present results of MHD axisymmetrical cylindrical simulations performed to study Hα emission maps from jets, with a toroidal field geometry for the magnetic field. Our code uses a linear Riemann solver, integrates equations in 2.5 dimensions and includes the calculation of the ionization fraction and the effects of the emission due to the collisional excitation of [O I] and [O II] lines, radiative recombination of H and the collisional ionization of H and excitation of Lyman-α. The simulations with variable ejection velocities show that the magnetic field produces an increase in the emission from all of the knots except for the first bow shock.  相似文献   

14.
Litvinenko  Yuri E. 《Solar physics》1999,188(1):115-123
The rate of two-dimensional flux pile-up magnetic reconnection is known to be severely limited by gas pressure in a low-beta plasma of the solar corona. As earlier perturbational calculations indicated, however, the pressure limitation should be less restrictive for three-dimensional flux pile-up. In this paper the maximum rate of reconnection is calculated in the approximation of reduced magnetohydrodynamics (RMHD), which is valid in the solar coronal loops. The rate is calculated for finite-magnitude reconnecting fields in the case of a strong axial field in the loop. Gas pressure effects are ignored in RMHD but a similar limitation on the rate of magnetic merging exists. Nevertheless, the magnetic energy dissipation rate and the reconnection electric field can increase by several orders of magnitude as compared with strictly two-dimensional pile-up. Though this is still not enough to explain the most powerful solar flares, slow coronal transients with energy release rates of order 1025– 1026 erg s–1and heating of quiet coronal loops are within the compass of the model.  相似文献   

15.
This paper describes a second-order upwind scheme for multidimensional magnetohydrodynamics, which uses a linear approximation for all Riemann problems except those involving strong rarefactions. This enables it to cope with initial data for which previously published schemes might fail. The condition ▽⊙ B  = 0 is not enforced in multidimensions, but the numerical problems associated with this are dealt with by adding source terms to the equations, as suggested by Powell. We also show that there are advantages to adding second-order artificial dissipation at shocks.  相似文献   

16.
The motion of a charged particle is studied within a magnetic field. This field consists of two separate fields; a dipole and a uniform magnetic field, parallel to dipole's magnetic moment. The present study is maintained by means of the adiabatic theory. We use a numerical integration of the equations of motion and give comparative results between the adiabatic theory and the numerical integration. The previous results are applied to the case of the Earth's open magnetosphere. Diagrams and tables support this application.  相似文献   

17.
We present an analytical model to explore the magnetic field turbulent spectrum by coupled high-frequency kinetic Alfvén wave (KAW) and slow mode of Alfvén wave (AW). The spectrum is computed as a realization of energy cascades from larger to smaller scales for a specific case of solar wind plasma at 1 AU. A two-fluid technique is implemented for the derivation of model equations leading two wave modes. These coupled, nonlinear equations are solved numerically. The nonlinearity in the system arises due to nonlinear ponderomotive force, which is believed to be responsible for the wave localization and magnetic islands formation. The numerical results show that the magnetic islands grow with time and attain a quasi-steady state after the modulation instability is saturated. The magnetic field spectrum and associated spectral indices are computed near the time of saturation of instability. The simulated spectrum in dispersion region follows a power-law with an index of ?2.5. The steeper spectrum could be attributed as energy transfer from larger to smaller scales and helps to study turbulence in solar wind. The magnetic field spectrum and spectral index show a good agreement with the observation of solar wind turbulent spectra.  相似文献   

18.
《New Astronomy》2007,12(5):398-409
We develop a numerical solver for radiative transfer problems based on the weighted essentially nonoscillatory (WENO) scheme modified with anti-diffusive flux corrections, in order to solve the temperature and ionization profiles around a point source of photons in the reionization epoch. Algorithms for such simulation must be able to handle the following two features: (1) the sharp profiles of ionization and temperature at the ionizing front (I-front) and the heating front (T-front), and (2) the fraction of neutral hydrogen within the ionized sphere is extremely small due to the stiffness of the rate equations of atom processes. The WENO scheme can properly handle these two features, as it has been shown to have high order of accuracy and good convergence in capturing discontinuities and complicated structures in fluid as well as to be significantly superior over piecewise smooth solutions containing discontinuities. With this algorithm, we show the time-dependence of the preheated shell around a UV photon source. In the first stage the I-front and T-front are coincident, and propagate with almost the speed of light. In later stage, when the frequency spectrum of UV photons is hardened, the speeds of propagation of the ionizing and heating fronts are both significantly less than the speed of light, and the heating front is always beyond the ionizing front. In the spherical shell between the I- and T-fronts, the IGM is heated, while atoms keep almost neutral. The time scale of the preheated shell evolution is dependent on the intensity of the photon source. We also find that the details of the pre-heated shell and the distribution of neutral hydrogen remained in the ionized sphere are actually sensitive to the parameters used. The WENO algorithm can provide stable and robust solutions to study these details.  相似文献   

19.
Many problems at the forefront of theoretical astrophysics require a treatment of dynamical fluid behavior. We present an efficient high-resolution shock-capturing hydrody-namic scheme designed to study such phenomena. We have implemented a weighted, essentially non-oscillatory (WENO) scheme to fifth order accuracy in space. HLLE approximate Riemann solver is used for the flux computation at cell interface, which does not require spectral decomposition into characteristic waves and so is computationally friendly. For time integration we apply a third order total variation diminishing (TVD) Runge-Kutta scheme. Extensive testing and comparison with schemes that require characteristic decomposition are carried out demonstrating the ability of our scheme to address challenging open questions in astrophysics.  相似文献   

20.
In this paper, the Space–Time Conservation Element and Solution Element (CESE) method is applied to 2.5-dimensional resistive magnetohydrodynamics (MHD) equations in Cartesian coordinates, with the purpose of modeling the magnetic reconnection study. To show the validity and capacity of its application to MHD reconnection problem, spontaneous fast reconnection and magnetic reconnection in multiple heliospheric current sheets are studied, which show good consistency with those obtained formerly by other authors. In order to assess the ∇ ⋅ B = 0 constraint numerically, the contours and evolution of ∇ ⋅ B are analyzed. The numerical results tell us that the CESE numerical scheme not only has good numerical resolution but also can keep the divergence-free condition for magnetic fields in the reconnection problems during the evolutionary process without any special treatment.  相似文献   

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