Lattice Boltzmann simulation of thermal nonideal fluids

Gonnella, Giuseppe; Lamura, A.; Sofonea, Victor

doi:10.1103/physreve.76.036703

Cited by 79 publications

(82 citation statements)

References 29 publications

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“…Since the functional derivative (17) is defined at constant e, a Lagrange multiplier field relative to e has to be introduced which can be identified with the temperature of equation (16). Equation (17) can be rewritten as…”

Section: Thermodynamicsmentioning

confidence: 99%

“…These expressions generalize to non-isothermal cases the relations given in [6] for binary mixtures. They could be conveniently used in the existing numerical schemes for the simulation of thermal fluids, as already done, for the case of van der Waals fluids, in [10,16]. In this paper, as examples of applications, we study interface profile behavior and phase separation neglecting the effects of the velocity field.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of binary mixtures in inhomogeneous temperatures

Gonnella¹,

Lamura²,

Piscitelli³

2008

J. Phys. A: Math. Theor.

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A dynamical description for fluid binary mixtures with variable temperature and concentration gradient contributions to entropy and internal energy is given. By using mass, momentum and energy balance equations together with the standard expression for entropy production, a generalized GibbsDuhem relation is obtained which takes into account thermal and concentration gradient contributions. Then an expression for the pressure tensor is derived. As examples of applications, interface behavior and phase separation have been numerically studied in two dimensions neglecting the contributions of the velocity field. In the simplest case with a constant thermal gradient, the growth exponent for the averaged size of domains is found to have the usual value z = 1/3 and the domains appear elongated in the direction of the thermal gradient. When the system is quenched by contact with external walls, the evolution of temperature profiles in the system is shown and the domain morphology is characterized by interfaces perpendicular to the thermal gradient.

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Section: Thermodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of binary mixtures in inhomogeneous temperatures

Gonnella¹,

Lamura²,

Piscitelli³

2008

J. Phys. A: Math. Theor.

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“…(10) is introduced to control the equilibrium properties of the liquid-vapor systems and allows to recover the following equations for VDW fluids [44],…”

Section: Gls Model For Multiphase Systemmentioning

confidence: 99%

“…This model is a further development of the one originally proposed by Watari and Tsutahara (WT) [9] and then developed by Gonnella, Lamura and Sofonea (GLS) [44]. The original WT model works only for ideal gas.…”

Section: Introductionmentioning

confidence: 99%

FFT-LB Modeling of Thermal Liquid-Vapor System

Gan

Zhang

et al. 2012

Commun. Theor. Phys.

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We further develop a thermal LB model for multiphase flows. In the improved model, we propose to use the windowed FFT and its inverse to calculate both the convection term and external force term. By using the new scheme, Gibbs oscillations can be damped effectively in unsmooth regions while the high resolution feature of the spectral method can be retained in smooth regions. As a result, spatiotemporal discretization errors are decreased dramatically and the conservation of total energy is much better preserved. A direct consequence of the improvements is that the unphysical spurious velocities at the interfacial regions can be damped to neglectable scale. With the new model, the phase diagram of the liquid-vapor system obtained from simulation is more consistent with that from theoretical calculation.Very sharp interfaces can be achieved. The accuracy of simulation results is also verified by the Laplace law. The high resolution, together with the low complexity of the FFT, endows the proposed method with considerable potential, for studying a wide class of problems in the field of multiphase flows and for solving other partial differential equations.

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“…A number of authors have investigated rigorous LB methods where the energy balance is recovered as the higher-order velocity moments of the discrete species distribution functions (mass and momentum are conserved by considering the firstand second-order velocity moments) [21][22][23][24]. But progress in these methods has been limited especially for thermal two-phase flows due to the high computational demands and numerical instabilities.…”

Section: Introductionmentioning

confidence: 99%

Lattice-Boltzmann-based two-phase thermal model for simulating phase change

et al. 2013

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A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum limit one recovers the well known macroscopic energy conservation equation for the mixtures. Heats of reaction, the enthalpy change associated with the phase change, and the diffusive transport of enthalpy are all taken into account; but the dependence of enthalpy on pressure, which is usually a small effect in most nonisothermal flows encountered in chemical reaction systems, is ignored. The energy equation is coupled to the LB equations for species transport and pseudopotential interaction forces through the EOS by using the filtered local pseudotemperature field. The proposed scheme is validated against simple test problems for which analytical solutions can readily be obtained.

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Lattice Boltzmann simulation of thermal nonideal fluids

Cited by 79 publications

References 29 publications

Dynamics of binary mixtures in inhomogeneous temperatures

Dynamics of binary mixtures in inhomogeneous temperatures

FFT-LB Modeling of Thermal Liquid-Vapor System

Lattice-Boltzmann-based two-phase thermal model for simulating phase change

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