10,158 research outputs found
ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics
We present a new numerical code, ECHO, based on an Eulerian Conservative High
Order scheme for time dependent three-dimensional general relativistic
magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at
providing a shock-capturing conservative method able to work at an arbitrary
level of formal accuracy (for smooth flows), where the other existing GRMHD and
GRMD schemes yield an overall second order at most. Moreover, our goal is to
present a general framework, based on the 3+1 Eulerian formalism, allowing for
different sets of equations, different algorithms, and working in a generic
space-time metric, so that ECHO may be easily coupled to any solver for
Einstein's equations. Various high order reconstruction methods are implemented
and a two-wave approximate Riemann solver is used. The induction equation is
treated by adopting the Upwind Constrained Transport (UCT) procedures,
appropriate to preserve the divergence-free condition of the magnetic field in
shock-capturing methods. The limiting case of magnetodynamics (also known as
force-free degenerate electrodynamics) is implemented by simply replacing the
fluid velocity with the electromagnetic drift velocity and by neglecting the
matter contribution to the stress tensor. ECHO is particularly accurate,
efficient, versatile, and robust. It has been tested against several
astrophysical applications, including a novel test on the propagation of large
amplitude circularly polarized Alfven waves. In particular, we show that
reconstruction based on a Monotonicity Preserving filter applied to a fixed
5-point stencil gives highly accurate results for smooth solutions, both in
flat and curved metric (up to the nominal fifth order), while at the same time
providing sharp profiles in tests involving discontinuities.Comment: 20 pages, revised version submitted to A&
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
Multiphysics simulations of collisionless plasmas
Collisionless plasmas, mostly present in astrophysical and space
environments, often require a kinetic treatment as given by the Vlasov
equation. Unfortunately, the six-dimensional Vlasov equation can only be solved
on very small parts of the considered spatial domain. However, in some cases,
e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a
localized domain and solve the remaining domain by appropriate fluid models. In
this paper, we describe a hierarchical treatment of collisionless plasmas in
the following way. On the finest level of description, the Vlasov equation is
solved both for ions and electrons. The next courser description treats
electrons with a 10-moment fluid model incorporating a simplified treatment of
Landau damping. At the boundary between the electron kinetic and fluid region,
the central question is how the fluid moments influence the electron
distribution function. On the next coarser level of description the ions are
treated by an 10-moment fluid model as well. It may turn out that in some
spatial regions far away from the reconnection zone the temperature tensor in
the 10-moment description is nearly isotopic. In this case it is even possible
to switch to a 5-moment description. This change can be done separately for
ions and electrons. To test this multiphysics approach, we apply this full
physics-adaptive simulations to the Geospace Environmental Modeling (GEM)
challenge of magnetic reconnection.Comment: 13 pages, 5 figure
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