56 research outputs found
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
Magnetohydrodynamics on an unstructured moving grid
Magnetic fields play an important role in astrophysics on a wide variety of
scales, ranging from the Sun and compact objects to galaxies and galaxy
clusters. Here we discuss a novel implementation of ideal magnetohydrodynamics
(MHD) in the moving mesh code AREPO which combines many of the advantages of
Eulerian and Lagrangian methods in a single computational technique. The
employed grid is defined as the Voronoi tessellation of a set of
mesh-generating points which can move along with the flow, yielding an
automatic adaptivity of the mesh and a substantial reduction of advection
errors. Our scheme solves the MHD Riemann problem in the rest frame of the
Voronoi interfaces using the HLLD Riemann solver. To satisfy the divergence
constraint of the magnetic field in multiple dimensions, the Dedner divergence
cleaning method is applied. In a set of standard test problems we show that the
new code produces accurate results, and that the divergence of the magnetic
field is kept sufficiently small to closely preserve the correct physical
solution. We also apply the code to two first application problems, namely
supersonic MHD turbulence and the spherical collapse of a magnetized cloud. We
verify that the code is able to handle both problems well, demonstrating the
applicability of this MHD version of AREPO to a wide range of problems in
astrophysics.Comment: 11 pages, 9 figures, accepted by MNRA
Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
We obtain renormalized sets of right and left eigenvectors of the flux vector
Jacobians of the relativistic MHD equations, which are regular and span a
complete basis in any physical state including degenerate ones. The
renormalization procedure relies on the characterization of the degeneracy
types in terms of the normal and tangential components of the magnetic field to
the wavefront in the fluid rest frame. Proper expressions of the renormalized
eigenvectors in conserved variables are obtained through the corresponding
matrix transformations. Our work completes previous analysis that present
different sets of right eigenvectors for non-degenerate and degenerate states,
and can be seen as a relativistic generalization of earlier work performed in
classical MHD. Based on the full wave decomposition (FWD) provided by the the
renormalized set of eigenvectors in conserved variables, we have also developed
a linearized (Roe-type) Riemann solver. Extensive testing against one- and
two-dimensional standard numerical problems allows us to conclude that our
solver is very robust. When compared with a family of simpler solvers that
avoid the knowledge of the full characteristic structure of the equations in
the computation of the numerical fluxes, our solver turns out to be less
diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The
amount of operations needed by the FWD solver makes it less efficient
computationally than those of the HLL family in one-dimensional problems.
However its relative efficiency increases in multidimensional simulations.Comment: 50 pages, 17 figures (2 in color). Submitted to ApJ Suppl. Se
On the application of Jacobian-free Riemann solvers for relativistic radiation magnetohydrodynamics under M1 closure
Radiative transfer plays a major role in high-energy astrophysics. In
multiple scenarios and in a broad range of energy scales, the coupling between
matter and radiation is essential to understand the interplay between theory,
observations and numerical simulations. In this paper, we present a novel
scheme for solving the equations of radiation relativistic magnetohydrodynamics
within the parallel code L\'ostrego. These equations, which are formulated
taking successive moments of the Boltzmann radiative transfer equation, are
solved under the gray-body approximation and the M1 closure using an IMEX time
integration scheme. The main novelty of our scheme is that we introduce for the
first time in the context of radiation magnetohydrodynamics a family of
Jacobian-free Riemann solvers based on internal approximations to the
Polynomial Viscosity Matrix, which were demonstrated to be robust and accurate
for non-radiative applications. The robustness and the limitations of the new
algorithms are tested by solving a collection of one-dimensional and
multi-dimensional test problems, both in the free-streaming and in the
diffusion radiation transport limits. Due to its stable performance, the
applicability of the scheme presented in this paper to real astrophysical
scenarios in high-energy astrophysics is promising. In future simulations, we
expect to be able to explore the dynamical relevance of photon-matter
interactions in the context of relativistic jets and accretion discs, from
microquasars and AGN to gamma-ray bursts.Comment: 21 pages, 13 figures. Accepted for publication in Computer Physics
Communication
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