General Equation Of State Research Articles

An HLLC-type Riemann solver and high-resolution Godunov method for a two-phase model of reactive flow with general equations of state

A high-resolution Godunov method is developed for a two-phase model of reactive flow. The model considers general equations of state of Mie-Grüneisen form and different choices for the reaction rate, both relevant for simulations of the dynamical behavior of detonations in PBX-type granular explosives. The numerical approach employs a Riemann solver, and various options ranging from an exact solver to an approximate solver of HLLC type are described. A principal aim of the paper is an assessment of the approximate Riemann solvers in terms of the accuracy and efficiency of numerical solutions of the two-phase model. In particular, this study considers the state-sensitive behavior in different regimes of the solutions in a reverse-impact configuration, including compaction, run to detonation, and the evolution to compaction-led and reaction-led steady detonations. For these regimes, the convergence properties of the numerical approach are examined for the different choices of the Riemann solver, as is the error in the solutions at lower grid resolution. Finally, the computational performance of the time-stepping scheme is assessed for the different solvers.

AUSM‐like expression of HLLC and its all‐speed extension

SummaryAdvection upstream splitting method (AUSM) and Harten‐Lax‐van Leer with contact (HLLC) are two popular families of flux functions. The AUSM is simple and requires no eigenstructure, which facilitates its extensions to general equations of state. Furthermore, one of its variants, simple low‐dissipation AUSM (SLAU), is applicable to all speeds and features removal of parameter setting by the user. HLLC, on the other hand, clearly defines three distinct waves in Riemann problem, namely, left‐running and right‐running acoustic waves, and entropy wave. This paper demonstrates that HLLC can be written in a very similar form with the AUSM family and that the similar manner in extending AUSM family to all speeds is easily incorporated into HLLC in this AUSM‐like form. Then, we combine the strengths of the both flux functions and offer a new inviscid numerical flux function within the framework of monotone upwind scheme for conservation laws (MUSCL) in computational fluid dynamics (CFD) for Euler and Navier‐Stokes equations. The resultant HLLC with low dissipation (HLLCL) numerical flux can compute low Mach number flows and sound propagations at the same time with high accuracy, as demonstrated by one‐dimensional and two‐dimensional numerical examples. Furthermore, the results indicate that its extensions to general fluids such as supercritical fluids are encouraging.

Nakedly singular counterpart of Schwarzschild\u2019s incompressible star. A barotropic continuity condition in the center

A static sphere of incompressible fluid with uniform proper energy density is considered as an example of exact star-like solution with weakened central regularity conditions characteristic of a nakedly singular spherical vaccuum solution. The solution is a singular counterpart of the Schwarzschild’s interior solution. The initial condition in the center for general barotropic equations of state is established.

Thermodynamics and phase transition in rotational Kiselev black hole

In this paper, we investigate the thermodynamic properties of rotational Kiselev black holes (KBH). Specifically, we use the first-order approximation of the event horizon (EH) to calculate thermodynamic properties for general equations of state [Formula: see text]. These thermodynamic properties include areas, entropies, horizon radii, surface gravities, surface temperatures, Komar energies and irreducible masses at the Cauchy horizon (CH) and EH. We study the products of these thermodynamic quantities, we find that these products are determined by the equation of state [Formula: see text] and strength parameter [Formula: see text]. In the case of the quintessence matter [Formula: see text], radiation [Formula: see text] and dust [Formula: see text], we discuss their properties in detail. We also generalize the Smarr mass formula and Christodoulou–Ruffini mass formula to rotational KBH. Finally, we study the phase transition and thermodynamic geometry for rotational KBH with radiation [Formula: see text]. Through analysis, we find that this phase transition is a second-order phase transition. Furthermore, we also obtain the scalar curvature in the thermodynamic geometry framework, indicating that the radiation matter may change the phase transition condition and properties for Kerr black hole.

Structural stability of shock waves in 2D compressible elastodynamics

We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic material in the sense of the local-in-time existence and uniqueness of discontinuous shock front solutions of the equations of compressible elastodynamics in two space dimensions. By the energy method based on a symmetrization of the wave equation and giving an a priori estimate without loss of derivatives for solutions of the constant coefficients linearized problem we find a condition sufficient for the uniform stability of rectilinear shock waves. Comparing this condition with that for the uniform stability of shock waves in isentropic gas dynamics, we make the conclusion that the elastic force plays stabilizing role. In particular, we show that, as in isentropic gas dynamics, all compressive shock waves are uniformly stable for convex equations of state. Moreover, for some particular deformations (and general equations of state), by the direct test of the uniform Kreiss–Lopatinski condition we show that the stability condition found by the energy method is not only sufficient but also necessary for uniform stability. As is known, uniform stability implies structural stability of corresponding curved shock waves.

Minimal geometric deformation in a Reissner\u2013Nordstr\xf6m background

This article is devoted to the study of new exact analytical solutions in the background of Reissner–Nordström space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general equation of state, relating the components of the theta -sector in order to obtain the new material contributions and the decoupler function f(r). Besides, we obtain the bounds on the free parameters of the extended solution to avoid new singularities. Furthermore, we show the finitude of all thermodynamic parameters of the solution such as the effective density {tilde{rho }}, radial {tilde{p}}_{r} and tangential {tilde{p}}_{t} pressure for different values of parameter alpha and the total electric charge Q. Finally, the behavior of some scalar invariants, namely the Ricci R and Kretshmann R_{mu nu omega epsilon }R^{mu nu omega epsilon } scalars are analyzed. It is also remarkable that, after an appropriate limit, the deformed Schwarzschild black hole solution always can be recovered.

Stable thin-shells from 5-dimensional extremal Einstein–Yang–Mills fields

By employing exact Einstein–Yang–Mills (EYM) solution in [Formula: see text] dimensions we establish spherical thin-shells with mass and Yang–Mills charge. Remarkably these shells are stable against linear, radial perturbations with a barotropic fluid presented on the shell with a generic equation of state [Formula: see text] supporting the speed of sound [Formula: see text].

Extension of the subgrid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities

Performing accurate large eddy simulations in compressible, turbulent magnetohydrodynamics (MHDs) is more challenging than in nonmagnetized fluids due to the complex interplay between kinetic, magnetic, and internal energy at different scales. Here, we extend the subgrid-scale gradient model, so far used in the momentum and induction equations, to also account for the unresolved scales in the energy evolution equation of a compressible ideal MHD fluid with a generic equation of state. We assess the model by considering box simulations of the turbulence triggered across a shear layer by the Kelvin-Helmholtz instability, testing cases where the small-scale dynamics cannot be fully captured by the resolution considered, such that the efficiency of the simulated dynamo effect depends on the resolution employed. This lack of numerical convergence is actually a currently common issue in several astrophysical problems, where the integral and fastest-growing-instability scales are too far apart to be fully covered numerically. We perform a priori and a posteriori tests of the extended gradient model. In the former, we find that, for many different initial conditions and resolutions, the gradient model outperforms other commonly used models in terms of correlation with the residuals coming from the filtering of a high-resolution run. In the second test, we show how a low-resolution run with the gradient model is able to quantitatively reproduce the evolution of the magnetic energy (the integrated value and the spectral distribution) coming from higher-resolution runs. This extension is the first step toward the implementation in relativistic MHDs.

Constraining values of bag constant for strange star candidates

We provide a strange star model under the framework of general relativity by using a general linear equation of state (EOS). The solution set thus obtained is employed on altogether 20 compact star candidates to constraint values of MIT bag model. No specific value of the bag constant ([Formula: see text]) a priori is assumed, rather possible range of values for bag constant is determined from observational data of the said set of compact stars. To do so, the Tolman–Oppenheimer–Volkoff (TOV) equation is solved by homotopy perturbation method (HPM) and hence we get a mass function for the stellar system. The solution to the Einstein field equations represents a nonsingular, causal and stable stellar structure which can be related to strange stars. Eventually, we get an interesting result on the range of the bag constant as [Formula: see text]. We have found the maximum surface redshift [Formula: see text] and shown that the central redshift ([Formula: see text]) cannot have value larger than [Formula: see text], where [Formula: see text]. Also, we provide a possible value of bag constant for neutron star with quark core using hadronic as well as quark EOS.

Nonlinear oscillations of ultra-cold atomic clouds in a magneto-optical trap

Confined atomic clouds in a magneto-optical trap can be formally interpreted as a single component trapped plasma. A hydrodynamical model in a three-dimensional geometry with radial symmetry is applied. A general polytropic equation of state is assumed. For suitable initial conditions and velocity fields, the Lagrangian variables method reduces the problem to ordinary differential equations in the limiting cases according to the prevalence of thermal or multiple-scattering (MS) effects. The thermal, pressure dominated case with adiabatic equation of state leads to a dissipative nonlinear oscillator with an inverse cubic force, in the form of a damped Pinney equation. An accurate approximate analytic solution derived from Kuzmak–Luke perturbation theory allows the assessment of the fully nonlinear dynamics. The applicability conditions of the two regimes are discussed. The intermediate case where both thermal and MS effects are equally relevant is also analytically studied.

Primordial gravitational waves in nonstandard cosmologies

Assuming that inflation is followed by a phase where the energy density of the Universe is dominated by a component with a general equation of state, we evaluate the spectrum of primordial gravitational waves induced in the post-inflationary Universe. We show that if the energy density of the Universe is dominated by a component $\phi$ before Big Bang nucleosynthesis, its equation of state could be constrained by gravitational wave experiments depending on the ratio of energy densities of $\phi$ and radiation, and also the temperature at the end of the $\phi$ dominated era. Also, we discuss the impact of scale dependence of tensor modes on the primordial gravitational wave spectrum during the $\phi$-domination. These models are motivated by beyond Standard Model physics and scenarios for non-thermal production of dark matter in the early Universe. We also constrain the parameter space of the tensor spectral index and the tensor-to-scalar ratio, using the experimental limits from gravitational wave experiments.

A relaxation scheme for a hyperbolic multiphase flow model

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

A conservative energy-momentum tensor in the f(R,T) gravity and its implications for the phenomenology of neutron stars

The solutions for the Tolmann-Oppenheimer-Volkoff (TOV) equation bring valuable informations about the macroscopical features of compact astrophysical objects as neutron stars. They are sensitive to both the equation of state considered for nuclear matter and the background gravitational theory. In this work we construct the TOV equation for a conservative version of the $f(R,T)$ gravity. While the non-vanishing of the covariant derivative of the $f(R,T)$ energy-momentum tensor yields, in a cosmological perspective, the prediction of creation of matter throughout the universe evolution as shown by T. Harko, in the analysis of the hydrostatic equilibrium of compact astrophysical objects, this property still lacks a convincing physical explanation. The imposition of $\nabla^{\mu}T_{\mu\nu}=0$ demands a particular form for the function $h(T)$ in $f(R,T)=R+h(T)$, which is here derived. Therefore, the choice of a specific equation of state for the star matter demands a unique form of $h(T)$, manifesting a strong connection between conserved $f(R,T)$ gravity and the star matter constitution. We construct and solve the TOV equation for the general equation of state for $p=k\rho^{\Gamma}$, with $k$ being the EoS parameter, $\rho$ {\it the energy density} and $\Gamma$ is the adiabatic index. We also derive the macroscopical properties of neutron stars ($\Gamma=5/3$) within this approach.

A Finite-Volume method for compressible non-equilibrium two-phase flows in networks of elastic pipelines using the Baer–Nunziato model

A novel Finite-Volume scheme for the numerical computations of compressible two-phase flows in pipelines is proposed for the fully non-equilibrium Baer–Nunziato model. The present FV approach is the extension of the method proposed in Daude and Galon (2018) in the context of the Euler equations to the Baer–Nunziato model. In addition, proper approximations of the non-conservative terms are proposed to consider jumps of volume fraction as well as jumps of cross-section in order to respect uniform pressure and velocity profiles preservation. In particular, focus is given to the numerical treatment of abrupt changes in area and to networks wherein several pipelines are connected at junctions. The proposed method makes it possible to avoid the use of an iterative procedure for the solution of the junction problem. The present approach can also deal with general Equations Of State. In addition, the fluid–structure interaction of compressible fluid flowing in flexible pipes is also considered. The proposed scheme is then assessed on a variety of shock-tubes and other transient flow problems and experiments demonstrating its capability to resolve such problems efficiently, accurately and robustly.

Constraining twin stars with GW170817

If a phase transition is allowed to take place in the core of a compact star, a new stable branch of equilibrium configurations can appear, providing solutions with the same mass as the purely hadronic branch and hence giving rise to twin-star configurations. We perform an extensive analysis of the features of the phase transition leading twin-star configurations and, at the same time, fulfilling the constraints coming from the maximum mass of $2M_\odot$ and the information following gravitational-wave event GW170817. In particular, we use a general equation of state for the neutron-star matter that parametrizes the hadron-quark phase transition between the model describing the hadronic phase and a constant speed of sound for the quark phase. We find that the largest number of twin-star solutions has masses in the neutron-star branch in the range $1-2M_\odot$ and twin-branch masses $\gtrsim 2M_\odot$. The analysis of the masses, radii and tidal deformabilities also reveals that when twin stars appear, the tidal deformability shows two distinct branches with the same mass, thus differing considerably from the behaviour expected for neutron stars. In addition, we find that the data from GW170817 is compatible with the existence of hybrid stars and could also be interpreted as produced by the merger of a binary system of hybrid stars or of a hybrid star with a neutron star. The presence of a hybrid star in the inspiral phase can be established clearly if future gravitational-wave detections measure chirp masses $\mathcal{M}\lesssim 1.2M_\odot$ and tidal deformabilities of $\Lambda_{1.4}\lesssim 400$ for $1.4M_\odot$ stars. Finally, combining all observational information available, we set constraints on the parameters that characterise the phase transition, the maximum masses, and the radii of $1.4M_\odot$ stars described by equations of state leading to twin-star configurations.

Asymptotically flat wormhole solutions with variable equation-of-state parameter

This paper discusses exact wormhole solutions in the framework of general relativity with a general equation of state that reduced to a linear equation of state asymptotically. By considering a special shape function, we find classes of solutions which are asymptotically flat. We study the violation of the null energy condition as the main ingredient in wormhole physics. The possibility of finding wormhole solutions with asymptotically different state parameter is investigated. We show that in principle, a wormhole with a vanishing redshift function and the selected shape function, cannot satisfy the null energy condition at a large distance from the wormhole. Our solutions have the positive total amount of matter in the ``volume integral quantifier'' method. For this class of solutions, fluid near the wormhole throat is in the phantom regime which at some $r={r}_{2}$, the phantom regime is connected to a distribution of dark energy regime. Thus, we need a small amount of exotic matter to construct wormhole solutions.

CMB constraints on dark matter phenomenology via reheating in minimal plateau inflation

We consider the CMB constraints on reheating and dark matter parameter space for a specific plateau type inflationary model. The plateau inflationary models which are currently most favored models from data can be well approximated by a potential of the form $V(\phi)\propto \phi^n$ around $\phi=0$. This fact makes it possible to study the reheating phase with general inflaton equation of state in a viable cosmological scenario. In addition, following our recent work[1], we generalize the connection between reheating and the present CMB data and the dark matter parameter space for general inflaton equation of state parameter.

Correlation of ionic liquid viscosity using Valderrama-Patel-Teja cubic equation of state and the geometric similitude concept. Part II: Binary mixtures of ionic liquids

The general equation of state employed in direct form, and for the first time presented in Part I of this series, is extended to correlate and predict the viscosity of binary mixtures of ionic liquids. The extension, also done for the first time, considers the classical mixing and combining rules commonly used in studies on pressure-temperature-volume equations of state, including two cases: (i) with no-interaction parameter (predictive model); and (ii) with one adjustable interaction parameter (correlating model). Data on viscosity of binary mixtures of ionic liquids have been gathered from the literature, analyzed, and selected, to finally construct a database of consistent data to obtain a general model that relates viscosity with pressure, temperature and concentration. A total of 2520 data points distributed on 344 isotherms, for 32 mixtures were considered for analysis, with average absolute relative deviations below 6%. If no interaction parameter is used, the model is still capable of predicting the viscosity of a mixture using only properties of the pure components. Results show that the model is accurate enough, being simpler and more accurate than sophisticated multiparametric models.

Solving the Riemann problem for realistic astrophysical fluids

We present new methods to solve the Riemann problem both exactly and approximately for general equations of state (EoS) to facilitate realistic modeling and understanding of astrophysical flows. The existence and uniqueness of the new exact general EoS Riemann solution can be guaranteed if the EoS is monotone regardless of the physical validity of the EoS. We confirm that: (1) the solution of the new exact general EoS Riemann solver and the solution of the original exact Riemann solver match when calculating perfect gas Euler equations; (2) the solution of the new Harten-Lax-van Leer-Contact (HLLC) general EoS Riemann solver and the solution of the original HLLC Riemann solver match when working with perfect gas EoS; and (3) the solution of the new HLLC general EoS Riemann solver approaches the new exact solution. We solve the EoS with two methods, one is to interpolate 2D EoS tables by the bi-linear interpolation method, and the other is to analytically calculate thermodynamic variables at run-time. The interpolation method is more general as it can work with other monotone and realistic EoS while the analytic EoS solver introduced here works with a relatively idealized EoS. Numerical results confirm that the accuracy of the two EoS solvers is similar. We study the efficiency of these two methods with the HLLC general EoS Riemann solver and find that analytic EoS solver is faster in the test problems. However, we point out that a combination of the two EoS solvers may become favorable in some specific problems. Throughout this research, we assume local thermal equilibrium.

A variational derivation of the thermodynamics of a moist atmosphere with rain process and its pseudoincompressible approximation

ABSTRACTIrreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation for moist atmospheric dynamics with rain process and subject to the irreversible processes of viscosity, heat conduction, diffusion, and phase transition. This derivation is based on a general variational formalism for nonequilibrium thermodynamics which extends Hamilton's principle to incorporate irreversible processes. It is valid for any state equation and thus also includes the treatment of the atmosphere of other planets. In this approach, the second law of thermodynamics is understood as a nonlinear constraint formulated with the help of new variables, called thermodynamic displacements, whose time derivative coincides with the thermodynamic force of the irreversible process. In order to cover the case of atmospheric dynamics, the original variational principle is extended in three directions in this paper: the inclusion of the rain process, the inclusion of phase changes, and the treatment of constraints. The variational formulation is written both in the Lagrangian and Eulerian descriptions and can be directly adapted to oceanic dynamics. The proposed variational formulation yields a general approach for the modelling of thermodynamically consistent models in atmospheric dynamics, thereby extending previous variational methods that were restricted to the reversible Hamiltonian case. We illustrate this point, by deriving a moist pseudoincompressible model with general equations of state and subject to the irreversible processes of viscosity, heat conduction, diffusion, and phase transition.