arXiv subjects

Livio Gibelli

Publications and source records attributed to Livio Gibelli.

13 recordsLinked to original sources

arXiv2026

Non-equilibrium evaporation of Lennard-Jones fluids: Enskog-Vlasov theory and Hertz-Knudsen model

Enskog-Vlasov equation is currently the most sophisticated kinetic model for describing non-equilibrium evaporative flows. While it enables more efficient simulations than the molecular dynamics (MD) methods, its accuracy in reproducing the flow properties of real fluids is limited by both the assumptions underlying the Vlasov forcing term and the approximation introduced by the Enskog collision term for short-range molecular interactions. To address this limitation, this work proposes a molecular kinetic model specifically designed for real fluids, with the Lennard-Jones fluids as an example. The model is first applied to evaluate the equilibrium characteristics of a liquid-vapour system, including the liquid-vapour coexistence curve, transport coefficients, vapour pressure, and surface tension coefficient. The results show excellent agreement with the MD simulation and experimental data. Furthermore, the model is used to investigate non-equilibrium evaporation, with a particular focus on the velocity distribution function adjacent to the liquid-vapour interface. The results confirm that deviations from the Maxwellian distribution persist in the vapour region, indicating limitations of the classical Hertz-Knudsen relation under pronounced non-equilibrium conditions. This work represents a critical step towards the development of an accurate and efficient computational framework for modelling non-equilibrium liquid-vapour flows for real fluids, with direct relevance to practical applications such as flow cooling.

cond-mat.soft↗

arXiv2024

uniGasFoam: a particle-based OpenFOAM solver for multiscale rarefied gas flows

This paper presents uniGasFoam, an open-source particle-based solver for multiscale rarefied gas flow simulations, which has been developed within the well-established OpenFOAM framework, and is an extension of the direct simulation Monte Carlo (DSMC) solver dsmcFoam+. The developed solver addresses the coupling challenges inherent in hybrid continuum-particle methods, originating from the disparate nature of finite-volume (FV) solvers found in computational fluid dynamics (CFD) software and DSMC particle solvers. This is achieved by employing alternative stochastic particle methods, resembling DSMC, to tackle the continuum limit. The uniGasFoam particle-particle coupling produces a numerical implementation that is simpler and more robust, faster in many steady-state flows, and more scalable for transient flows compared to conventional continuum-particle coupling. The presented framework is unified and generic, and can couple DSMC with stochastic particle (SP) and unified stochastic particle (USP) methods, or be employed for pure DSMC, SP, and USP gas simulations. To enhance user experience, optimise computational resources and minimise user error, advanced adaptive algorithms such as transient adaptive sub-cells, non-uniform cell weighting, and adaptive global time stepping have been integrated into uniGasFoam. In this paper, the hybrid USP-DSMC module of uniGasFoam is rigorously validated through multiple benchmark cases, consistently showing excellent agreement with pure DSMC, hybrid CFD-DSMC, and literature results. Notably, uniGasFoam achieves significant computational gains compared to pure dsmcFoam+ simulations, rendering it a robust computational tool well-suited for addressing multiscale rarefied gas flows of engineering importance.

physics.flu-dyn↗

arXiv2023

A DSMC-CFD coupling method using surrogate modelling for low-speed rarefied gas flows

A new Micro-Macro-Surrogate (MMS) hybrid method is presented that couples the Direct Simulation Monte Carlo (DSMC) method with Computational Fluid Dynamics (CFD) to simulate low-speed rarefied gas flows. The proposed MMS method incorporates surrogate modelling instead of direct coupling of DSMC data with the CFD, addressing the limitations CFD has in accurately modelling rarefied gas flows, the computational cost of DSMC for low-speed and multiscale flows, as well as the pitfalls of noise in conventional direct coupling approaches. The surrogate models, trained on the DSMC data using Bayesian inference, provide noise-free and accurate corrections to the CFD simulation enabling it to capture the non-continuum physics. The MMS hybrid approach is validated by simulating low-speed, force-driven rarefied gas flows in a canonical parallel-plate system and shows excellent agreement with DSMC benchmark results. A comparison with the typical domain decomposition DSMC-CFD hybrid method is also presented, to demonstrate the advantages of noise-avoidance in the proposed approach. The method also inherently captures the uncertainty arising from micro-model fluctuations, allowing for the quantification of noise-related uncertainty in the predictions. The proposed MMS method demonstrates the potential to enable multiscale simulations where CFD is inaccurate and DSMC is prohibitively expensive.

physics.flu-dyn↗

arXiv2021

On the velocity distribution function of spontaneously evaporating atoms

Numerical solutions of the Enskog-Vlasov (EV) equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity components normal and parallel to the liquid-vapor interface. The drift velocity and the temperature anisotropy reduce as the liquid bulk temperature decreases but persist for relatively low temperatures corresponding to a vapor behaviour which is only slightly non-ideal. Deviations from the undrifted isotropic half-Maxwellian are shown to be consequences of collisions in the liquid-vapor interface which preferentially backscatter atoms with lower normal-velocity component.

physics.flu-dyn↗

arXiv2020

Active particles methods towards modeling in science and society

This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors by differential models. The contents is in three parts. Firstly, we derive the mathematical method; subsequently, we show how the method can be applied in a number of case studies related to well defined living systems and finally, we look ahead to research perspectives focusing both on mathematical methods and further applications.

cond-mat.soft↗

arXiv2017

On the Interplay between Behavioral Dynamics and Social Interactions in Human Crowds

This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living, hence complex, system. The analysis looks at real physical situations where safety problems might arise in some specific circumstances. The approach is based on the methods of the kinetic theory of active particles. Computational applications enlighten the role of human behaviors.

physics.soc-ph↗

arXiv2015

Stochastic Evolving Differential Games Toward a Systems Theory of Behavioral Social Dynamics

This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living evolutionary ensemble composed by many individuals, who express specific strategies, cooperate, compete and might aggregate into groups which pursue a common interest. A critical analysis on the complexity features of social system is developed and a differential structure is derived to provide a general framework toward modeling.

physics.soc-ph↗

arXiv2015

First Order Models of Human Crowds with Behavioral-Social Dynamics

This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional process by which walking individuals select their velocity direction. Crowd heterogeneity is modeled by dividing the whole system into subsystems identified by different features. The passage from one subsystem to the other is induced by interactions. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. The paper also proposes a system approach to the modeling of the dynamics in complex venues, where individuals move through areas with different features.

physics.soc-ph↗

arXiv2014

Toward a Mathematical Theory of Behavioral-Social Dynamics for Pedestrian Crowds

This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. The main feature of this approach is a detailed analysis of the interactions between dynamics and social behaviors.

physics.soc-ph↗

arXiv2013

A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization

A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of a Gauss-Hermite quadrature. This is defined by means of half- and/or full-range Hermite polynomials depending whether or not the distribution function presents a discontinuity in the velocity space. The resulting semi-discrete Boltzmann equation is in the form of a system of hyperbolic partial differential equations whose solution can be obtained by standard numerical approaches. The spectral rate of convergence of the results in the velocity space is shown by solving the spatially uniform homogeneous relaxation to equilibrium of Maxwell molecules. As an application, the two-dimensional cavity flow of a gas composed by hard-sphere molecules is studied for different Knudsen and Mach numbers. Although computationally demanding, the proposed method turns out to be an effective tool for studying low-speed slightly rarefied gas flows.

physics.comp-ph↗

arXiv2010

Solving the Boltzmann Equation on GPU

We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo evaluation of the collision integral. The efficiency of the code is demonstrated by solving the two-dimensional driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential code of two order of magnitudes. This makes the proposed method of solution a viable alternative to particle simulations for studying unsteady low Mach number flows.

physics.comp-ph↗

arXiv2009

Solving Kinetic Equations on GPUs I: Model Kinetic Equations

We present an algorithm specifically tailored for solving kinetic equations onto GPUs. The efficiency of the algorithm is demonstrated by solving the one-dimensional shock wave structure problem and a two-dimensional low Mach number driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential codes of two order of magnitudes. The algorithm can easily be extended to three-dimensional flows and more general collision models.

physics.comp-ph↗

arXiv2008

A Catastrophe-Theoretic Approach to Tricritical Points with Application to Liquid Crystals

A criterion to locate tricritical points in phase diagrams is proposed. The criterion is formulated in the framework of the Elementary Catastrophe Theory and encompasses all the existing criteria in that it applies to systems described by a generally non symmetric free energy which can depend on one or more order parameters. We show that a tricritical point is given whenever the free energy is not 4-determined. An application to smectic-C liquid crystals is briefly discussed.

cond-mat.soft↗