A parallel adaptive mesh refinement (AMR) scheme is described for solving the hyperbolic system of partial-differential equations governing ideal magnetohydrodynamic (MHD) flows in three space dimensions. This highly parallelized algorithm adopts a cell-centered upwind finite-volume discretization procedure and uses limited solution reconstruction, approximate Riemann solvers, and explicit mult...

Magnetohydrodynamics MHD concerns the motion of a conducting fluid in an electromagnetic field with a very wide range of applications. The dynamic motion of the fluids and the magnetic field strongly interact each other, and thus, both the hydrodynamic and electrodynamic effects have to be considered. The governing equations of the plane magnetohydrodynamic compressible flows have the following...

A general framework that incorporates the Iroshnikov-Kraichnan (IK) and Goldreich-Sridhar (GS) phenomenalogies of magnetohydrodynamic (MHD) turbulence is developed. This affords a clarification of the regimes of validity of IK and GS phenomenalogies and hence help resolve some controversies in this problem. Magnetohydrodynamic (MHD) flows that occur naturally (like astrophysical situations) and...

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high β) and magnetically dominated (low β) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a techni...

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high β) and magnetic pressure dominated (low β) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a t...

Context: Numerical simulations of MHD accretion flows in the vicinity of a supermasssive black hole provide important insights to the problem of why and how systems – such as the Galactic Center – are underluminous and variable. In particular, the simulations indicate that low angular momentum accretion flow is strongly variable both quantitatively and qualitatively. This variability and a rela...

The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate that the theoretical stability properties are valid in practice with negligible compromises to accuracy. The result is a highly robust scheme with state-of-t...

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a nonlinear Riemann solver for ideal MHD, which includes rarefactions as well as shocks an...

We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro-and magne-tohydrodynamic (MHD) flows. Numerical simulations were performed with up to 1024 3 collocation points and 10 million particles in the Navier-Stokes case and 512 3 collocation points and 1 million particles in the MHD case. In the hydrodynamics case our ...