The limiting behavior of the Riemann solution to the isentropic Euler system for logarithmic equation of state with a source term

2021 ◽  
Author(s):  
Anupam Sen ◽  
T. Raja Sekhar
Keyword(s):  
Equation Of State ◽  
Source Term ◽  
Euler System ◽  
Limiting Behavior ◽  
Riemann Solution ◽  
Logarithmic Equation

A virtual force method to rectify the equation of state of the lattice Boltzmann models

2021 ◽  
pp. 2250025
Author(s):  
Abed Zadehgol
Keyword(s):  
Equation Of State ◽  
Kinetic Model ◽  
Lattice Boltzmann ◽  
Source Term ◽  
Force Method ◽  
Modified Method ◽  
Virtual Force ◽  
Error Terms ◽  
High Mach ◽  
Lattice Boltzmann Models

In this work, to rectify the equation of state (EOS) of a recently introduced constant speed entropic kinetic model (CSKM), a virtual force method is proposed. The CSKM, as shown in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)] and Zadehgol [Phys. Rev. E 91, 063311 (2015)], is an entropic kinetic model with unconventional entropies of Burg and Tsallis. The dependence of the pressure on the velocity, in the CSKM, was addressed and it was shown that it can be rectified by inserting rest particles into the model. This work shows that this dependence can also be removed by treating the pressure gradient as a pseudo force term, expanding the source term using the Fourier series, and applying the modified method of Khazaeli et al. [Phys. Rev. E 98, 053303 (2018)]. The proposed method can potentially be used to remove other pseudo-force error terms of the CSKM, e.g. the residual error terms which become significant at high Mach numbers, ensuring thermodynamic consistency of the entropic model, at the compressible flow regimes. The accuracy of the method is verified by simulating benchmark flows.

Influence of thermal radiation on singular behavior of the Universe

2021 ◽  
pp. 128-133
Author(s):  
A.N. Makarenko ◽  
◽  
A.V. Timoshkin ◽  
Keyword(s):  
Equation Of State ◽  
Thermal Radiation ◽  
Thermal Effects ◽  
Qualitative Change ◽  
Viscous Fluids ◽  
Singular Behavior ◽  
Viscosity Property ◽  
Big Rip ◽  
Logarithmic Equation ◽  
The Universe

Cosmological models with inhomogeneous viscous fluids with a logarithmic equation of state in the Friedmann-Lemaitre-Robertson-Walker universe are considered. The influence of thermal effects caused by Hawking radiation on the visible horizon of the Universe on the change in the type of singularity of the dark Universe is investigated. It is shown that under the influence of thermal radiation, taking into account the viscosity property of a dark fluid, a qualitative change in the type of the Big Rip singularity is possible, which can lead to the absence of a singularity in the Universe at all.

scholarly journals Turning Point Principle for Relativistic Stars

2021 ◽  
Vol 387 (2) ◽  
pp. 729-759
Author(s):  
Mahir Hadžić ◽  
Zhiwu Lin
Keyword(s):  
Equation Of State ◽  
Gravitational Collapse ◽  
Turning Point ◽  
Euler System ◽  
Gravitation Theory ◽  
Spherically Symmetric ◽  
University Of Chicago ◽  
Relativistic Stars ◽  
The University ◽  
University Of Chicago Press

AbstractUpon specifying an equation of state, spherically symmetric steady states of the Einstein-Euler system are embedded in 1-parameter families of solutions, characterized by the value of their central redshift. In the 1960’s Zel’dovich (Voprosy Kosmogonii 9:157–170, 1963) and Harrison et al. (Gravitation Theory and Gravitational Collapse. The University of Chicago press, Chicago, 1965) formulated a turning point principle which states that the spectral stability can be exchanged to instability and vice versa only at the extrema of mass along the mass-radius curve. Moreover the bending orientation at the extrema determines whether a growing mode is gained or lost. We prove the turning point principle and provide a detailed description of the linearized dynamics. One of the corollaries of our result is that the number of growing modes grows to infinity as the central redshift increases to infinity.

A logarithmic equation of state

1998 ◽  
Vol 109 (1-2) ◽  
pp. 1-8 ◽  
Author(s):  
J.-P Poirier ◽  
A Tarantola
Keyword(s):  
Equation Of State ◽  
Logarithmic Equation

scholarly journals The Convergence of Riemann Solutions to the Modified Chaplygin Gas Equations with a Coulomb-Like Friction Term as the Pressure Vanishes

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Yongqiang Fan ◽  
Lihui Guo ◽  
Gan Yin
Keyword(s):  
Source Term ◽  
Chaplygin Gas ◽  
Euler System ◽  
Modified Chaplygin Gas ◽  
Riemann Solutions ◽  
Delta Shock ◽  
Vacuum States ◽  
Friction Term ◽  
Self Similar ◽  
Delta Shock Waves

This paper studies the convergence of Riemann solutions to the inhomogeneous modified Chaplygin gas equations as the pressure vanishes. The delta shock waves and vacuum states occur as the pressure vanishes. The Riemann solutions of inhomogeneous modified Chaplygin gas equations are no longer self-similar. It is obviously different from the Riemann solutions of homogeneous modified Chaplygin gas equations. When the pressure vanishes, the Riemann solutions of the modified Chaplygin gas equations with a coulomb-like friction term converge to the Riemann solutions of the pressureless Euler system with a source term.

scholarly journals Viscous accelerating universe with nonlinear and logarithmic equation of state fluid

2019 ◽  
Vol 16 (10) ◽  
pp. 1950150
Author(s):  
I. Brevik ◽  
A. N. Makarenko ◽  
A. V. Timoshkin
Keyword(s):  
Equation Of State ◽  
Accelerated Expansion ◽  
Accelerating Universe ◽  
Late Time ◽  
Viscosity Effects ◽  
Logarithmic Equation ◽  
The Universe ◽  
Gravitational Equations ◽  
Universe Evolution ◽  
Friedmann Robertson Walker

We describe the accelerated expansion of the late-time universe using a generalized equation of state (EoS) when account is taken of bulk viscosity. We assume a homogeneous and isotropic Friedmann–Robertson–Walker spacetime. Solutions of the gravitational equations for dark energy are obtained in implicit form. Characteristic properties of the universe evolution in the presence of the viscosity effects are discussed. Finally, the dynamics of the accelerated expansion of the viscous universe are discussed on the basis of a modified logarithmic-corrected EoS.

Sign in / Sign up

Export Citation Format

Share Document