arXiv subjects

Victor Sofonea

Publications and source records attributed to Victor Sofonea.

12 recordsLinked to original sources

arXiv2025

Thermal Enskog-Vlasov Lattice Boltzmann model with phase separation

An Enskog-Vlasov finite-difference Lattice Boltzmann (EV-FDLB) for liquid-vapor systems with variable temperature is introduced. The model involves both the simplified Enskog collision operator and the self-consistent force field which accounts for the long-range interaction between the fluid particles. Full-range Gauss-Hermite quadratures were used for the discretization of the momentum space. The numerical solutions of the Enskog-Vlasov equation obtained employing the EV-FDLB model and the Direct Simulation Monte Carlo (DSMC)-like particle method (PM) are compared. Reasonable agreement is found between the two approaches when simulating the liquid-vapor phase separation and the liquid slab evaporation.

physics.flu-dyn↗

arXiv2024

Growth regimes in three-dimensional phase separation of liquid-vapor systems

The liquid-vapor phase separation is investigated via lattice Boltzmann simulations in three dimensions. After expressing length and time scales in reduced physical units, we combined data from several large simulations (on $512^3$ nodes), with different values of viscosity, surface tension and temperature, to obtain a single curve of rescaled length $\hat{l}$ as a function of rescaled time $\hat{t}$. We find evidence of the existence of kinetic and inertial regimes with growth exponents $α_d=1/2$ and $α_i=2/3$ over several time decades, with a crossover from $α_d$ to $α_i$ at $\hat{t} \simeq 1$. This allows us to rule out the existence of a viscous regime with $α_v=1$ in three-dimensional liquid-vapor isothermal phase separation, differently from what happens in binary fluid mixtures. An in-depth analysis of the kinetics of the phase separation process, as well as a characterization of the morphology and the flow properties, are further presented in order to provide clues into the dynamics of the phase-separation process.

cond-mat.soft↗

arXiv2023

Bounded flows of dense gases

Numerical solutions of the Enskog equation obtained employing a Finite-Difference Lattice Boltzmann (FDLB) and a Direct Simulation Monte Carlo (DSMC)-like particle method (PM) are systematically compared to determine the range of applicability of the simplified Enskog collision operator implemented in the Lattice Boltzmann framework. Three types of bounded flows of dense gases - namely the Fourier, the Couette, and the Poiseuille flows - are investigated for a wide range of input parameters. For low to moderate reduced density, the proposed FDLB model exhibits commendable accuracy for all bounded flows tested in this study, with substantially lower computational cost than the PM method.

physics.flu-dyn↗

arXiv2020

Comparison of the Shakhov and ellipsoidal models for the Boltzmann equation and DSMC for ab initio-based particle interactions

In this paper, we consider the capabilities of the Boltzmann equation with the Shakhov and ellipsoidal models for the collision term to capture the characteristics of rarefied gas flows. The benchmark is performed by comparing the results obtained using these kinetic model equations with direct simulation Monte Carlo (DSMC) results for particles interacting via ab initio potentials. The analysis is restricted to channel flows between parallel plates and we consider three flow problems, namely: the heat transfer between stationary plates, the Couette flow and the heat transfer under shear. The simulations are performed in the non-linear regime for the 3He, 4He, and Ne gases. The reference temperature ranges between 1 K and 3000 K for 3He and 4He and between 20 K and 5000 K for Ne. While good agreement is seen up to the transition regime for the direct phenomena (shear stress, heat flux driven by temperature gradient), the relative errors in the cross phenomena (heat flux perpendicular to the temperature gradient) exceed 10% even in the slip-flow regime. The kinetic model equations are solved using the finite difference lattice Boltzmann algorithm based on half-range Gauss-Hermite quadratures with the third order upwind method used for the implementation of the advection.

physics.comp-ph↗

arXiv2019

Comparison between isothermal collision-streaming and finite-difference lattice Boltzmann models

We present here a comparison between collision-streaming and finite-difference lattice Boltzmann (LB) models. This study provides a derivation of useful formulae which help one to properly compare the simulation results obtained with both LB models. We consider three physical problems: the shock wave propagation, the damping of shear waves, and the decay of Taylor-Green vortices, often used as benchmark tests. Despite the different mathematical and computational complexity of the two methods, we show how the physical results can be related to obtain relevant quantities.

physics.comp-ph↗

arXiv2019

Lattice Boltzmann approach to rarefied gas flows using half-range Gauss-Hermite quadratures: Comparison to DSMC results based on ab initio potentials

In this paper, we employ the lattice Boltzmann method to solve the Boltzmann equation with the Shakhov model for the collision integral in the context of the 3D planar Couette flow. The half-range Gauss-Hermite quadrature is used to account for the wall-induced discontinuity in the distribution function. The lattice Boltzmann simulation results are compared with direct simulation Monte Carlo (DSMC) results for ${}^3{\rm He}$ and ${}^4{\rm He}$ atoms interacting via ab initio potentials, at various values of the rarefaction parameter $δ$, where the temperature of the plates varies from $1\ {\rm K}$ up to $3000\ {\rm K}$. Good agreement is observed between the results obtained using the Shakhov model and the DSMC data at large values of the rarefaction parameter. The agreement deteriorates as the rarefaction parameter is decreased, however we highlight that the relative errors in the non-diagonal component of the shear stress do not exceed $2.5\%$.

physics.comp-ph↗

arXiv2018

Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term

The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the walls, respectively. The ability of our models to simulate rarefied flows are validated through comparison against previously reported results obtained using the linearized Boltzmann-BGK equation for values of the Knudsen number (Kn) up to $100$. We find that recovering the non-linear part of the velocity profile (i.e., its deviation from a linear function) at ${\rm Kn} \gtrsim 1$ requires high quadrature orders. We then employ the Shakhov model for the collision term to obtain macroscopic profiles for Maxwell molecules using the standard $μ\sim T^ω$ law, as well as for monatomic Helium and Argon gases, modeled through ab-initio potentials, where the viscosity is recovered using the Sutherland model. We validate our implementation by comparison with DSMC results and find excellent match for all macroscopic quantities for ${\rm Kn} \lesssim 0.1$. At ${\rm Kn} \gtrsim 0.1$, small deviations can be seen in the profiles of the diagonal components of the pressure tensor, the heat flux parallel to the plates, and the velocity profile, as well as in the values of the velocity gradient at the channel center. We attribute these deviations to the limited applicability of the Shakhov collision model for highly out of equilibrium flows.

physics.flu-dyn↗

arXiv2017

Implementation of the force term in half-range lattice Boltzmann models

In the frame of the Boltzmann equation, wall-bounded flows of rarefied gases require the implementation of boundary conditions at the kinetic level. Such boundary conditions induce a discontinuity in the distribution function with respect to the component of the momentum which is normal to the boundary. Expanding the distribution function with respect to half-range polynomials allows this discontinuity to be captured. The implementation of this concept has been reported in the literature only for force-free flows. In the case of general forces which can have non-zero components in the direction perpendicular to the walls, the implementation of the force term requires taking the momentum space gradient of a discontinuous function. Our proposed method deals with this difficulty by employing the theory of distributions. We validate our procedure by considering the simple one-dimensional flow between diffuse-reflective walls of equal or different temperatures driven by the constant gravitational force. For this flow, a comparison between the results obtained with the full-range and the half-range Gauss-Hermite LB models is also presented.

physics.flu-dyn↗

arXiv2017

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

We develop a two-dimensional Lattice Boltzmann model for liquid-vapour systems with variable temperature. Our model is based on a single particle distribution function expanded with respect to the full-range Hermite polynomials. In order to ensure the recovery of the hydrodynamic equations for thermal flows, we use a fourth order expansion together with a set of momentum vectors with 25 elements whose Cartesian projections are the roots of the Hermite polynomial of order Q = 5. Since these vectors are off-lattice, a fifth-order projection scheme is used to evolve the corresponding set of distribution functions. A fourth order scheme employing a 49 point stencil is used to compute the gradient operators in the force term that ensures the liquid-vapour phase separation and diffuse reflection boundary conditions are used on the walls. We demonstrate at least fourth order convergence with respect to the lattice spacing in the contexts of shear and longitudinal wave propagation through the van der Waals fluid. For the planar interface, fourth order convergence can be seen at small enough lattice spacings, while the effect of the spurious velocity on the temperature profile is found to be smaller than 1.0%, even when T w ' 0.7 T c . We further validate our scheme by considering the Laplace pressure test. Galilean invariance is shown to be preserved up to second order with respect to the background velocity. We further investigate the liquid-vapour phase separation between two parallel walls kept at a constant temperature T w smaller than the critical temperature T c and discuss the main features of this process.

physics.flu-dyn↗

arXiv2003

Reduction of spurious velocity in finite difference lattice Boltzmann models for liquid - vapor systems

The origin of the spurious interface velocity in finite difference lattice Boltzmann models for liquid - vapor systems is related to the first order upwind scheme used to compute the space derivatives in the evolution equations. A correction force term is introduced to eliminate the spurious velocity. The correction term helps to recover sharp interfaces and sets the phase diagram close to the one derived using the Maxwell construction.

nlin.CG↗

arXiv1995

Lattice Boltzmann Model For Magnetic Fluids

A lattice Boltzmann model with interacting particles was developed in order to simulate the magneto-rheological characteristics of magnetic fluids. In the frame of this model, $6\, +\,1$ species of particles are allowed to move across a $2D$ triangular lattice. Among these species, $6$ of them carry an individual magnetic dipole moment and interact themselves not only as a result oflocal collisions, as in current Lattice Boltzmann models, but also as a result of nearest neighbours magnetic dipole-dipole interaction. The relative distribution of the individual magnetic moments is determined by the intensity of an external static magnetic field acting on the whole system. This model exhibits some relevant characteristics of real magnetic fluids, i.e., anisotropic structure formation as a result of magnetic field induced gas-liquid phase transition and magnetic field dependence of the sound velocity and the attenuation coefficient.

comp-gas↗

arXiv1995

Lattice Boltzmann Approach to Viscous Flows Between Parallel Plates

Four different kinds of laminar flows between two parallel plates are investigated using the Lattice Boltzmann Method (LBM). The LBM accuracy is estimated in two cases using numerical fits of the parabolic velocity profiles and the kinetic energy decay curves, respectively. The error relative to the analytical kinematic viscosity values was found to be less than one percent in both cases. The LBM results for the unsteady development of the flow when one plate is brought suddenly at a constant velocity, are found in excellent agreement with the analytical solution. Because the classical Schlichting's approximate solution for the entrance--region flow is not valid for small Reynolds numbers, a Finite Element Method solution was used in order to check the accuracy of the LBM results.

comp-gas↗