Related papers: A new shock-capturing numerical scheme for ideal h…
This paper proposes a novel numerical method based on Godunov Smoothed Particle Hydrodynamics for special relativistic fluid dynamics. Our method utilizes a Riemann solver to describe shock, enhancing accuracy in strong shock waves. The…
In this article, we present a state-of-the-art algorithm for solving the relativistic viscous hydrodynamics equation with the QCD equation of state. The numerical method is based on the second-order Godunov method and has less numerical…
In this paper we present a full general relativistic one-dimensional hydro-code which incorporates a modern high-resolution shock-capturing algorithm, with an approximate Riemann solver, for the correct modelling of formation and…
We construct a new Godunov type relativistic hydrodynamics code in Milne coordinates, using a Riemann solver based on the two-shock approximation which is stable under the existence of large shock waves. We check the correctness of the…
We assess the suitability of a recent high-resolution central scheme developed by Kurganov & Tadmor (2000) for the solution of the relativistic hydrodynamics equations. The novelty of this approach relies on the absence of Riemann solvers…
We present a second-order upwind numerical scheme for equations of relativistic hydrodynamics with a source term. A new non-linear Riemann solver is constructed. Solution of a Riemann problem on a cells boundary is based on exact relations…
In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations…
High resolution, non-oscillatory, central difference (NOCD) numerical schemes are introduced as alternatives to more traditional artificial viscosity (AV) and Godunov methods for solving the fully general relativistic hydrodynamics…
Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first…
Some of the most interesting scenarios that can be studied in astrophysics, contain fluids and plasma moving under the influence of strong gravitational fields. To study these problems it is required to implement numerical algorithms robust…
In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…
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 investigate the Riemann problem for the shallow water equations with variable and (possibly) discontinuous topography and provide a complete description of the properties of its solutions: existence; uniqueness in the non-resonant…
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…
In this paper, we present an approach to solving the Riemann problem in one-dimensional relativistic hydrodynamics, where the most computationally expensive steps of the exact solver are replaced by compact, highly specialized neural…
We introduce what we call a locally inertial Godunov method with dynamical time dilation, and use it to simulate a new one parameter family of general relativistic shock wave solutions of the Einstein equations for a perfect fluid. The…
We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify…
Multidimensional shock-capturing numerical schemes for special relativistic hydrodynamics (RHD) are computationally more expensive than their correspondent Euler versions, due to the nonlinear relations between conservative and primitive…
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary…
We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from nonrelativistic to relativistic (shock, contact discontinuity, and Alfv\'en wave).…