Related papers: Revisiting Hyperbolicity of Relativistic Fluids
We present a new computational method for smoothly matching general relativistic ideal magnetohydrodynamics (MHD) to its force-free limit. The method is based on a flux-conservative formalism for MHD and its force-free limit, and a vector…
Binary systems of compact objects with electromagnetic field are modeled by helically symmetric Einstein-Maxwell spacetimes with charged and magnetized perfect fluids. Previously derived thermodynamic laws for helically-symmetric…
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
The force-free limit of magnetohydrodynamics (MHD) is often a reasonable approximation to model black hole and neutron star magnetospheres. We describe a general relativistic force-free (GRFFE) formulation that allows general relativistic…
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two…
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity are dissipative regularizations. We propose a minimal, local, conservative, nonlinear, dispersive regularization of…
We consider selected topics of relativistic superfluidity within gauge/string duality. Non-relativistically, the only conservation law relevant to the hydrodynamic approximation is the energy-momentum conservation. Relativistically, one has…
A new formulation of time-dependent Relaxed Magnetohydrodynamics (RxMHD) is derived variationally from Hamilton's Action Principle using microscopic conservation of mass, and macroscopic conservation of total magnetic helicity, cross…
We present a fully Lagrangian conservation form of the general relativistic hydrodynamic equations for perfect fluids with artificial viscosity in a given arbitrary background spacetime. This conservation formulation is achieved by choosing…
We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Rung-Kutta…
The hydrodynamic description of a superfluid is usually based on a two-fluid picture. In this thesis, basic properties of such a relativistic two-fluid system are derived from the underlying microscopic physics of a complex scalar quantum…
A third order shock-capturing numerical scheme for three-dimensional special relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against several numerical tests. The simple and efficient central scheme described in Paper…
Ideal systems of equations such as Euler and MHD may develop singular structures like shocks, vortex/current sheets. Among these, vortical singularities arise due to vortex stretching which can lead to unbounded growth of enstrophy.…
We consider a framework for non-ideal magnetohydrodynamics in general relativity, paying particular attention to the physics involved. The discussion highlights the connection between the microphysics (associated with a given equation of…
General-relativistic magnetohydrodynamic (GRMHD) simulations are an important tool to study a variety of astrophysical systems such as neutron star mergers, core-collapse supernovae, and accretion onto compact objects. A conservative GRMHD…
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper we propose a minimal, local, conservative,…
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we…
In this paper, we consider the 3-D compressible isentropic radiation hydrodynamics (RHD) equations. The local existence of strong solutions with vacuum is firstly established when the initial data is arbitrarily large, contains vacuum and…
Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this…
Relativistic hydrodynamics of an isentropic fluid in a gravitational field is considered as the particular example from the family of Lagrangian hydrodynamic-type systems which possess an infinite set of integrals of motion due to the…