Related papers: Lagrangian versus Eulerian Methods for Toroidally-…
In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the time step is sharply limited by the Courant condition. Also, because the mean flow speed with…
The magnetohydrodynamical behavior (MHD) of accretion disks is reviewed. A detailed presentation of the fundamental MHD equations appropriate for protostellar disks is given. The combination of a weak (subthermal) magnetic field and…
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The…
Eulerian hydrodynamical simulations are a powerful and popular tool for modeling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We…
We numerically evolve turbulence driven by the magnetorotational instability (MRI) in a 3D, unstratified shearing box and study its structure using two-point correlation functions. We confirm Fromang and Papaloizou's result that shearing…
Numerical simulations of the air in the atmosphere and water in the oceans are essential for numerical weather prediction. The state-of-the-art for performing these fluid simulations relies on an Eulerian viewpoint, in which the fluid…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
In simulations of viscously evolving accretion disks, the inner boundary condition is particularly important. If treated incorrectly, it induces incorrect behavior very quickly, because the viscous time is shortest near the inner boundary.…
We use global magnetohydrodynamic simulations to study the influence of net vertical magnetic fields on the structure of geometrically thin ($H/r \approx 0.05$) accretion disks in the Newtonian limit. We consider initial mid-plane gas to…
We investigate the dynamics of the accretion disks of young stars with fossil large-scale magnetic field. The author's magnetohydrodynamic (MHD) model of the accretion disks is generalized to consider the dynamical influence of the magnetic…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
The above comment http://dx.doi.org/10.1088/0953-8984/22/42/428001 and a previous letter by the same author reveal a great misunderstanding of what Eulerian and Lagrangian quantities are, and a confusion between the deformation of an…
We present the results of local, vertically stratified, radiation MHD shearing box simulations of MRI turbulence appropriate for the hydrogen ionizing regime of dwarf nova and soft X-ray transient outbursts. We incorporate the…
In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…
For an accurate description of electromagneto-thermomechanical systems, electromagnetic fields need to be described in a Eulerian frame, whereby the thermomechanics is solved in a Lagrangean frame. It is possible to map the Eulerian frame…
Magnetorotational turbulence provides a viable mechanism for angular momentum transport in accretion disks. We present global, three dimensional (3D), MHD accretion disk simulations that investigate the dependence of the turbulent stresses…
Magnetohydrodynamic (MHD) turbulence driven by the magnetorotational instability can provide diffusive transport of angular momentum in astrophysical disks, and a widely studied computational model for this process is the ideal, stratified,…
Polarisation measurements by the Event Horizon Telescope from M87$^{\ast}$ and Sgr A$^\ast$ suggest that there is a dynamically strong, ordered magnetic field, typical of what is expected of a magnetically arrested accretion disk (MAD). In…
Lagrangian tracer particles have long been used to track the history of individual gas parcels in hydrodynamical codes. Particles advected by the cell-centered velocity carry no representation of underlying numerical diffusion, and thus…
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…