Related papers: Special relativistic spherically symmetric Lagrang…
We derive the special and general relativistic hydrodynamic equations of motion for ideal fluids from a variational principle. Our approach allows to find approximate solutions, whenever physically motivated trial functions can be used.…
We present a general and practical procedure to solve the general relativistic hydrodynamic equations by using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows.…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…
We present a new complete set of Lagrangian relativistic hydrodynamical equations describing the transfer of energy and momentum between a standard fluid and a radiation fluid in a general non-stationary spherical flow. The new set of…
The new formal analogy between superfluid systems and cosmology, which emerges by taking into account the back-reaction of the vacuum to the quanta of sound waves \cite{noi}, enables us to put forward some common features between these two…
The paper proposes a second-order accurate direct Eulerian generalized Riemann problem (GRP) scheme for the spherically symmetric general relativistic hydrodynamical (RHD) equations and a second-order accurate discretization for the…
The description of general relativistic radiation hydrodynamics in spherical symmetry is presented in natural coordinate choices. For hydrodynamics, comoving coordinates are chosen, and the momentum phase space for the radiation particles…
In this paper we test a special-relativistic formulation of Smoothed Particle Hydrodynamics (SPH) that has been derived from the Lagrangian of an ideal fluid. Apart from its symmetry in the particle indices, the new formulation differs from…
The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes…
We present a new methodology for simulating self-gravitating general-relativistic fluids. In our approach the fluid is modelled by means of Lagrangian particles in the framework of a general-relativistic (GR) Smooth Particle Hydrodynamics…
We present the derivation of hydrodynamical equations for a perfect fluid in General Relativity, within the 3+1 decomposition of spacetime framework, using only primitive variables. Primitive variables are opposed to conserved variables, as…
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation…
The objective of this work is to revisit fundamental aspects of relativistic hydrodynamics, aiming at the construction of a first course in relativistic hydrodynamics and its applications to astrophysics at the level of end of undergraduate…
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution…
An implicit Lagrangian hydrodynamics code for general relativistic spherical collapse is presented. This scheme is based on an approximate linearized Riemann solver (Roe type scheme). This code is aimed especially at the calculation of the…
In this paper we report on what we believe is the first successful implementation of relativistic hydrodynamics, coupled to dynamical spacetimes, in spherical polar coordinates without symmetry assumptions. We employ a high-resolution…
We present a numerical method to solve the equations of general relativistic hydrodynamics in a given external gravitational field. The method is based on a generalization of Roe's approximate Riemann solver for the non relativistic Euler…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so called the renormalization-group (RG) method. A macroscopic frame…
In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a…