Related papers: DISPATCH methods: an approximate, entropy-based Ri…
The applicability of relativistic magnetohydrodynamics (RMHD) and its generalization to two-fluid models (including the Hall and inertial effects) is systematically investigated by using the method of dominant balance in the two-fluid…
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…
The transport of energy through radiation is very important in many astrophysical phenomena. In dynamical problems the time-dependent equations of radiation hydrodynamics have to be solved. We present a newly developed…
The paper investigates the use of low-diffusion (contact-discontinuity-resolving [Liou M.S.: {\em J. Comp. Phys.} {\bf 160} (2000) 623--648]) approximate Riemann solvers for the convective part of the Reynolds-averaged Navier-Stokes…
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 demonstrate that the shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Additionally, we show that the classical Newtonian slip friction and Manning…
We introduce a generalization of Glimm's random choice method, which provides us with an approximation of entropy solutions to quasilinear hyperbolic system of balance laws. The flux-function and the source term of the equations may depend…
In this note we consider the ideal compressible magneto-hydrodynamics (MHD) equations in a special two dimensional setting. We show that there exist particular initial data for which one obtains infinitely many entropy-conserving weak…
We study the motion of isentropic gas in nozzles. This is a major subject in fluid dynamics. In fact, the nozzle is utilized to increase the thrust of rocket engines. Moreover, the nozzle flow is closely related to astrophysics. These…
Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,CDL2} have demonstrated that entropy solutions may not be…
The paper proposes a way to control the viscosity of numerical approximation in the contact SPH method. This variant of SPH contains momentum and energy fluxes in the right-hand sides of the equations, which are calculated using the…
For the inertial Qian-Sheng model of nematic liquid crystals in the $Q$-tensor framework, we illustrate the roles played by the entropy inequality and energy dissipation in the well-posedness of smooth solutions when we employ energy…
We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while…
We propose a general class of genuinely two-dimensional incomplete Riemann solvers for systems of conservation laws. In particular, extensions of Balsara's multidimensional HLL scheme [J. Comput. Phys. 231 (2012) 7476-7503] to…
Whether the global existence and uniqueness of strong solutions of $n$-dimensional incompressible magnetohydrodynamic (MHD for short) equations with only kinematic viscosity or magnetic diffusion holds true or not remains an outstanding…
This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and…
In this paper, the second in a series, we document the algorithms and solvers for compressible nonrelativistic hydrodynamics implemented in GenASiS (General Astrophysical Simulation System)---a new code being developed initially and…
We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show…
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…
The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and…