The Experts below are selected from a list of 1371 Experts worldwide ranked by ideXlab platform
Tommaso Ruggeri - One of the best experts on this subject based on the ideXlab platform.
-
production terms in relativistic extended thermodynamics of Gas with internal structure via a new bgk model
Annals of Physics, 2019Co-Authors: Maria Cristina Carrisi, Sebastiano Pennisi, Tommaso RuggeriAbstract:Abstract The goal of this paper is to obtain a precise expression for the production tensor in a dissipative hyperbolic relativistic theory of Gas with internal structure. For this aim, we use a variant of relativistic BGK model for the Boltzmann–Chernikov kinetic equation. Moreover, we deduce some inequalities for the coefficients requiring the entropy principle and the convexity of entropy density. As a limiting case, the expression of the production tensor in the case of Monatomic Gas is also evaluated.
-
Second-order approximation of extended thermodynamics of a Monatomic Gas and hyperbolicity region
Continuum Mechanics and Thermodynamics, 2019Co-Authors: Francesca Brini, Tommaso RuggeriAbstract:The rational extended thermodynamics theory describes non-equilibrium phenomena for rarefied Gases, and it is usually approximated in the neighborhood of an equilibrium state. Consequently, the hyperbolicity of its differential system holds only in some domain of the state variables (called hyperbolicity region). In this paper, we present a second-order approximation with respect to non-equilibrium variables, in the case of a Monatomic Gas theory with 13 fields. We verify that, in the case of one-dimensional space, the radius of the hyperbolicity region is larger than the corresponding radius of the first-order approximation. Moreover, when the model involves three-dimensional field variables, we prove that the equilibrium state for differential systems with quadratic approximation is inside the hyperbolicity region. This fact is in contrast with the first-order models that, in some cases of three-dimensional field variables, present the equilibrium point at the boundary of the hyperbolicity region.
-
relativistic eulerian rarefied Gas with internal structure
Journal of Mathematical Physics, 2018Co-Authors: Sebastiano Pennisi, Tommaso RuggeriAbstract:Recently Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] proposed a casual hyperbolic model for a dissipative relativistic Gas with internal structure. In this paper, we consider the particular case of the model when dissipation is negligible (Eulerian Gas). We study in particular the energy behavior in comparison with the Synge energy which is valid for Monatomic Gas and we evaluate the characteristic velocities proving the hyperbolicity of the differential system. The second part of the paper is devoted to the ultra-relativistic limit of the model and we prove that there exists a critical value of the degree of freedom such that for smaller values of this quantity the ultra-relativistic limit of the energy of a Gas with structure is the same as the Synge energy, while for larger degrees of freedom the energy increases with the degree of freedom itself.
-
non linear extended thermodynamics of real Gases with 6 fields
International Journal of Non-linear Mechanics, 2015Co-Authors: Takashi Arima, Tommaso Ruggeri, Masaru Sugiyama, Shigeru TaniguchiAbstract:Abstract We establish extended thermodynamics (ET) of real Gases with 6 independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. We prove its compatibility with the universal principles (the entropy principle, the Galilean invariance and the stability), and obtain the symmetric hyperbolic system with respect to the main field. In near-equilibrium we recover the previous results. The correspondence between the ET 6-field theory and Meixner׳s theory of relaxation processes is discovered. The internal variable and the non-equilibrium temperature in Meixner׳s theory are expressed in terms of the quantities of the ET 6-field theory, in particular, the dynamic pressure. As an example, we present the cases of a rarefied polyatomic Gas and study the Monatomic-Gas limit where the system converges to the Euler system of a perfect fluid.
-
Extended thermodynamics of rarefied polyatomic Gases and characteristic velocities
2014Co-Authors: Takashi Arima, Andrea Mentrelli, Tommaso RuggeriAbstract:Extended Thermodynamics of rarefied polyatomic Gases is characterized by two hi- erarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a particle is taken into account. To obtain the closed set of the field equations for the system with many moments and for an arbitrary entropy functional that includes degenerate Gases, the entropy principle and maximum entropy principle are studied and the equivalence of these two methods is shown as in the well-established case of the Monatomic Gas. In addition the recent results of the present theory are summarized. On the basis of physical considerations, the truncation orders of the two hierarchies are seen to be not independent on each other. The equilibrium characteristic velocities of the emerging hyperbolic system of partial di¤erential equations are analyzed and com- pared to those of Monatomic Gases. Inspection shows that the lower bound estimate of the maximum equilibrium characteristic velocity valid for Monatomic Gases, which increases as the truncation order increases, is valid for any rarefied polyatomic Gas
Jason M. Reese - One of the best experts on this subject based on the ideXlab platform.
-
A fast spectral method for the Boltzmann equation for Monatomic Gas mixtures
Journal of Computational Physics, 2015Co-Authors: Jun Zhang, Jason M. Reese, Yonghao ZhangAbstract:Although the fast spectral method has been established for solving the Boltzmann equation for single-species Monatomic Gases, its extension to Gas mixtures is not easy because of the non-unitary mass ratio between the different molecular species. The conventional spectral method can solve the Boltzmann collision operator for binary Gas mixtures but with a computational cost of the order m r 3 N 6 , where m r is the mass ratio of the heavier to the lighter species, and N is the number of frequency nodes in each frequency direction. In this paper, we propose a fast spectral method for binary mixtures of Monatomic Gases that has a computational cost O ( m r M 2 N 4 log ? N ) , where M 2 is the number of discrete solid angles. The algorithm is validated by comparing numerical results with analytical Bobylev-Krook-Wu solutions for the spatially-homogeneous relaxation problem, for m r up to 36. In spatially-inhomogeneous problems, such as normal shock waves and planar Fourier/Couette flows, our results compare well with those of both the numerical kernel and the direct simulation Monte Carlo methods. As an application, a two-dimensional temperature-driven flow is investigated, for which other numerical methods find it difficult to resolve the flow field at large Knudsen numbers. The fast spectral method is accurate and effective in simulating highly rarefied Gas flows, i.e. it captures the discontinuities and fine structures in the velocity distribution functions.
-
a volume based hydrodynamic approach to sound wave propagation in a Monatomic Gas
Physics of Fluids, 2010Co-Authors: Kokou S Dadzie, Jason M. ReeseAbstract:We investigate sound wave propagation in a Monatomic Gas using a volume-based hydrodynamic model. In Dadzie et al. [Physica A 387, 6079 (2008)], a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a mass-density diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number (high frequency) regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the “sound waves” presumed in the experiments may be better thought of as “mass-density waves,” rather than pressure waves.
-
a volume based hydrodynamic approach to sound wave propagation in a Monatomic Gas
arXiv: Fluid Dynamics, 2009Co-Authors: Kokou S Dadzie, Jason M. ReeseAbstract:We investigate sound wave propagation in a Monatomic Gas using a volume-based hydrodynamic model. In Physica A vol 387(24) (2008) pp6079-6094, a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a mass-density diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number (high frequency) regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the "sound waves" presumed in the experiments may be better thought of as "mass-density waves", rather than the pressure waves of the continuum regime.
Yonghao Zhang - One of the best experts on this subject based on the ideXlab platform.
-
multiscale simulation of molecular Gas flows by the general synthetic iterative scheme
Computer Methods in Applied Mechanics and Engineering, 2021Co-Authors: Yonghao ZhangAbstract:Abstract The in-depth knowledge of rarefied Gas dynamics is crucial to address challenges in a wide range of engineering problems, where Gas flows are usually multiscale, i.e., covering a wide range of Knudsen numbers. As the traditional Navier–Stokes equations fail, Gas kinetic equations are required to model the flows. So far, very few numerical methods are designed to efficiently solve the multiscale Gas dynamics and reveal the role of internal degrees of freedom of Gas molecules. In this work, a general synthetic iterative scheme (GSIS) is proposed to find steady-state solutions of the Gas kinetic equations for molecular Gas flows accurately and efficiently, where the Gas kinetic equations are solved together with the macroscopic synthetic equations that expedite solutions towards the steady state. In the macroscopic synthetic equations, while the momentum equation is the same as that used in the GSIS for Monatomic Gas, two energy equations are introduced here for polyatomic Gases: one is for the translational energy and the other for the internal energy; these equations are derived exactly from the Gas kinetic equations hence no approximation is made in final solutions. The Fourier stability analysis is performed to show that the GSIS permits fast convergence to steady-state solutions in the entire flow regime; meanwhile the asymptotic analysis shows that the GSIS recovers the Navier–Stokes equations when the Knudsen number is small, even on the spatial grid with cell size much larger than the molecular mean free path. With all these unique features, several challenging numerical examples are given to show that the proposed GSIS is a promising tool to simulate multiscale molecular Gas flows and investigate the effects of internal degrees of freedom.
-
A fast spectral method for the Boltzmann equation for Monatomic Gas mixtures
Journal of Computational Physics, 2015Co-Authors: Jun Zhang, Jason M. Reese, Yonghao ZhangAbstract:Although the fast spectral method has been established for solving the Boltzmann equation for single-species Monatomic Gases, its extension to Gas mixtures is not easy because of the non-unitary mass ratio between the different molecular species. The conventional spectral method can solve the Boltzmann collision operator for binary Gas mixtures but with a computational cost of the order m r 3 N 6 , where m r is the mass ratio of the heavier to the lighter species, and N is the number of frequency nodes in each frequency direction. In this paper, we propose a fast spectral method for binary mixtures of Monatomic Gases that has a computational cost O ( m r M 2 N 4 log ? N ) , where M 2 is the number of discrete solid angles. The algorithm is validated by comparing numerical results with analytical Bobylev-Krook-Wu solutions for the spatially-homogeneous relaxation problem, for m r up to 36. In spatially-inhomogeneous problems, such as normal shock waves and planar Fourier/Couette flows, our results compare well with those of both the numerical kernel and the direct simulation Monte Carlo methods. As an application, a two-dimensional temperature-driven flow is investigated, for which other numerical methods find it difficult to resolve the flow field at large Knudsen numbers. The fast spectral method is accurate and effective in simulating highly rarefied Gas flows, i.e. it captures the discontinuities and fine structures in the velocity distribution functions.
Ruggeri Tommaso - One of the best experts on this subject based on the ideXlab platform.
-
Hyperbolicity of first and second order extended thermodynamics theory of polyatomic rarefied Gases
'Elsevier BV', 2020Co-Authors: Brini Francesca, Ruggeri TommasoAbstract:The balance laws of Rational Extended Thermodynamics describe well the evolution of rarefied Gases in non-equilibrium. Usually, it is necessary to approximate the theory in a neighborhood of an equilibrium state andconsequently, its hyperbolicity property remains valid only in a neighborhood of the equilibrium state of thefield variables, calledhyperbolicityregion. The goal of this paper is first to determine the differential system with14 fields for a rarefied polyatomic polytropic Gas, approximated at the second-order in the non-equilibriumvariables. Then, we investigate and compare the hyperbolicity property of the first-order and second-ordersystems. In particular, we analyze the role played by the dynamic pressure and the molecular degrees offreedom. Finally, we also show that in the Monatomic singular limit the quadratic theory for a polyatomic Gasconverges to the corresponding quadratic theory for a Monatomic Gas
-
Ultra-relativistic limit of extended thermodynamics of rarefied polyatomic Gas
Dipartimento di Matematica e Informatica, 2019Co-Authors: Pennisi Sebastiano, Ruggeri TommasoAbstract:The aim of this paper is to evaluate the ultra-relativistic limit of a recent causal theory proposed for polyatomic dissipative relativistic Gas. The explicitly expression of characteristic velocities of the hyperbolic system is found in term of the degree of freedom of the Gas and compared with the one of Monatomic Gas
-
On the sub-shock formation in extended thermodynamics
'Elsevier BV', 2017Co-Authors: Taniguchi Shigeru, Ruggeri TommasoAbstract:In hyperbolic dissipative systems, the solution of the shock structure is not always continuous and a discontinuous part (sub-shock) appears when the velocity of the shock wave is greater than a critical value. In principle, the sub-shock may occur when the shock velocity $s$ reaches one of the characteristic eigenvalues of the hyperbolic system. Nevertheless, Rational Extended Thermodynamics (ET) for a rarefied Monatomic Gas predicts the sub-shock formation only when $s$ exceeds the maximum characteristic velocity of the system evaluated in the unperturbed state $\lambda^{\max}_0$. This fact agrees with a general theorem asserting that continuous shock structure cannot exist for $s >\lambda^{\max}_0 $. In the present paper, first, the shock structure is numerically analyzed on the basis of ET for a rarefied polyatomic Gas with $14$ independent fields. It is shown that, also in this case, the shock structure is still continuous when $s$ meets characteristic velocities except for the maximum one and therefore the sub-shock appears only when $s >\lambda^{\max}_0 $. This example reinforces the conjecture that, the differential systems of ET theories have the special characteristics such that the sub-shock appears only for $s$ greater than the unperturbed maximum characteristic velocity. However, in the second part of the paper, we construct a counterexample of this conjecture by using a simple $2 \times 2$ hyperbolic dissipative system which satisfies all requirements of ET. In contrast to previous results, we show the clear sub-shock formation with a slower shock velocity than the maximum unperturbed characteristic velocity.Comment: 13 pages, 8 figure
-
Non-linear extended thermodynamics of real Gases with 6 fields
2015Co-Authors: Arima Takashi, Ruggeri Tommaso, Sugiyama Masaru, Taniguchi ShigeruAbstract:Received 5 February 2015 Accepted 5 February 2015 Available online 13 February 2015 Keywords: Extended thermodynamics Non-equilibrium thermodynamics of Gases Meixner's theory Dynamic pressure 1. Introduction Rational extended thermodynamics [1] (hereafter referred to as ET)1 is a thermodynamic theory that is applicable to non-equilibrium phenomena with steep gradients and rapid changes in space–time, which may be out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations. As ET has been strictly related to the kinetic theory with the closure method of the hierarchy of moment equations, the applic- ability range of the theory has been restricted within rarefied Monatomic Gases. Only recently, however, the ET theory of dense Gases and of polyatomic rarefied Gases has been successfully devel- oped by the present authors obtaining a 14-field theory that, in the limit of small relaxation times (parabolic limit), reduces to the Navier– Stokes–Fourier classical theory [2]. This new approach to the case of polyatomic rarefied Gases, in particular, is in perfect agreement with the closure procedure using the Maximum Entropy Principle (MEP) at the kinetic level in which the distribution function depends on an extra variable that takes into account the influence of degrees of freedom of a molecule on energy transfer during collisions [3]. n Corresponding author. E-mail addresses: arima@kanagawa-u.ac.jp (T. Arima), tommaso.ruggeri@unibo.it (T. Ruggeri), sugiyama@nitech.ac.jp (M. Sugiyama), taniguchi.shigeru@kct.ac.jp (S. Taniguchi). 1 Rational extended thermodynamics is sometimes referred to as RET in order to distinguish it from other approaches in extended thermodynamics. However, in this paper, we use, for simplicity, the acronym ET for indicating rational extended thermodynamics. http://dx.doi.org/10.1016/j.ijnonlinmec.2015.02.005 0020-7462/& 2015 Elsevier Ltd. All rights reserved. abstract We establish extended thermodynamics (ET) of real Gases with 6 independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approxima- tion. We prove its compatibility with the universal principles (the entropy principle, the Galilean invariance and the stability), and obtain the symmetric hyperbolic system with respect to the main field. In near- equilibrium we recover the previous results. The correspondence between the ET 6-field theory and Meixner's theory of relaxation processes is discovered. The internal variable and the non-equilibrium temperature in Meixner's theory are expressed in terms of the quantities of the ET 6-field theory, in particular, the dynamic pressure. As an example, we present the cases of a rarefied polyatomic Gas and study the Monatomic-Gas limit where the system converges to the Euler system of a perfect fluid
-
Rational extended thermodynamics beyond the Monatomic Gas
Springer International Publishing, 2015Co-Authors: Ruggeri Tommaso, Sugiyama MasaruAbstract:Rational Extended Thermodynamics beyond the Monatomic Gas September 14, 2015, Pages 1-376 Rational extended thermodynamics beyond the Monatomic Gas (Book) Ruggeri, T.a, Sugiyama, M.b a Dept. of Mathematics and Res., Center of Applied Mathematics AM2, University of Bologna, Bologna, Italy b Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan View references (538) Abstract This book is dedicated to the recent developments in RET with the aim to explore polyatomic Gas, dense Gas and mixture of Gases in non-equilibrium. In particular we present the theory of dense Gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic Gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecules internal degrees of freedom. Recent results on mixtures of Gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied Monatomic Gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena
Patrick Jenny - One of the best experts on this subject based on the ideXlab platform.
-
fokker planck model for computational studies of Monatomic rarefied Gas flows
Journal of Fluid Mechanics, 2011Co-Authors: M H Gorji, Manuel Torrilhon, Patrick JennyAbstract:In this study, we propose a non-linear continuous stochastic velocity process for simulations of Monatomic Gas flows. The model equation is derived from a Fokker–Planck approximation of the Boltzmann equation. By introducing a cubic non-linear drift term, the model leads to the correct Prandtl number of 2/3 for Monatomic Gas, which is crucial to study heat transport phenomena. Moreover, a highly accurate scheme to evolve the computational particles in velocity- and physical space is devised. An important property of this integration scheme is that it ensures energy conservation and honours the tortuosity of particle trajectories. Especially in situations with small to moderate Knudsen numbers, this allows to proceed with much larger time steps than with direct simulation Monte Carlo (DSMC), i.e. the mean collision time not necessarily has to be resolved, and thus leads to more efficient simulations. Another computational advantage is that no direct collisions have to be calculated in the proposed algorithm. For validation, different micro-channel flow test cases in the near continuum and transitional regimes were considered. Detailed comparisons with DSMC for Knudsen numbers between 0.07 and 2 reveal that the new solution algorithm based on the Fokker–Planck approximation for the collision operator can accurately predict molecular stresses and heat flux and thus also Gas velocity and temperature profiles. Moreover, for the Knudsen Paradox, it is shown that good agreement with DSMC is achieved up to a Knudsen number of about 5.