arXiv subjects

Alexander J. Wagner

Publications and source records attributed to Alexander J. Wagner.

At least 19 recordsLinked to original sources

arXiv2026

Molecular dynamics perspectives on nonideal fluid models for the lattice Boltzmann method

Despite their widespread use, mesoscopic models for non-ideal fluids have rarely been systematically validated against microscopic simulations. In this work, molecular dynamics (MD) simulations of confined fluids are mapped onto a mesoscopic framework, enabling direct comparison with lattice Boltzmann (LBM) formulations. By analyzing the moments of the distribution function, we identify a force formulation that consistently reproduces the microscopic statistics and macroscopic force balance. The results show that a hybrid formulation combining pseudo-potential and free-energy approaches provides the most consistent description. These findings establish a direct link between microscopic particle dynamics and mesoscopic modeling, offering practical guidance for the development and selection of LBM models for non-ideal and multiphase flows.

physics.flu-dyn↗

arXiv2025

Convection can enhance the capacitive charging of porous electrodes

Charge transport in porous electrodes is foundational for modern energy storage technologies like supercapacitors, fuel cells, and batteries. Supercapacitors in particular rely solely on storing energy in charged pores. Here, we simulate the charging of a single electrolyte-filled pore using the modified Poisson-Nernst-Planck and Navier-Stokes equations. We find that electroconvection can substantially speed up the charging dynamics. We uncover the fundamental mechanism of electroconvection during pore charging through an analytical model that predicts the induced flow field and the electric current arising due to convection. Our findings suggest that convection is especially important in the limit of slender pores with thin electric double layers, and becomes significant beyond a certain threshold voltage that is an inherent electrolyte property.

cond-mat.soft↗

arXiv2025

Mirror states enable lower viscosity lattice gases

We developed a method for significantly lowering the viscosity achievable for a hydrodynamic lattice gas method. The key advance is the derivation of a mirror state that allows for a reduction of viscosity by more than an order of magnitude over existing lattice gas methods.

physics.flu-dyn↗

arXiv2025

Integer Lattice Gas with a sampling collision operator for the fluctuating Navier-Stokes Equation

This paper constitutes a step in the direction of developing integer lattice gas methods as an attractive alternative to lattice Boltzmann methods. Here we show that to Boltzmann limit the one dimensional Blommel integer lattice gas is very close to entropic lattice Boltzmann. More interestingly the integer lattice gas retains additional correlations that prevent the existence of a well defined Boltzmann limit. In the analysis of the decaying sine wave we will see that in some situations the bulk viscosity can crucially depend on such correlations beyond the Boltzmann limit. A sampling collision operator, introduced here, can speed up the execution time to make the algorithm obtain comparable computational efficiency to entropic lattice Boltzmann methods.

physics.flu-dyn↗

arXiv2025

Analytical solution for dynamic evaporation of liquid in isothermal condition

An analytical solution based on a diffuse interface model is presented for an isothermal evaporation problem under sub-saturation pressure. The macroscopic equations are derived from the free-energy method, widely recognized in the lattice Boltzmann literature, distinguishing our approach from conventional evaporation models that rely on jump conditions or pure kinetic theory. The interface behavior is fully described by differential equations, eliminating the need for assumptions such as local equilibrium at the interface. We derive an exact analytical solution for the inviscid case and propose an approximate solution when viscosity effects are considered. Our model unveils a novel relationship between evaporation rate and viscosity, providing new insights that have not been thoroughly explored in the literature. The analytical results are validated through numerical simulations using the open-source parallel library OpenLB, demonstrating excellent agreement in predicting the physical behavior of the evaporation phenomena within the framework of diffuse interface methods.

physics.flu-dyn↗

arXiv2025

A Method for Analytical Solutions in the Lattice Boltzmann Method

Analytical solutions to the lattice Boltzmann Equation make it possible to study the method itself, explore the properties of its collision operator, and identify implementations of boundary conditions. In this paper, we propose a method to find analytical solutions where the macroscopic flow profile is known. We test this method on bulk Couette flow aligned and inclined to the simulation lattice with the quadratic and entropic equilibrium distributions. Our method indeed provides an analytical solution to these flows when using the quadratic distribution. When the flow is aligned to the lattice, our method provides an analytical solution using the entropic distribution for practical relaxation times and shear rates. We show that a small even order truncation of the formal solution is optimal for accuracy-compute-time trade-off. In the inclined case, our method does not conserve momentum, by a small relative error, when using the entropic distribution. We also discover that entropic lattice Boltzmann method is not compatible with the angled Couette flow. We discuss the application of our method to more complicated flows.

physics.flu-dyn↗

arXiv2023

Effects of gravity induced pressure variations for thermal liquid-gas phase-change simulations with the pseudopotential lattice Boltzmann method

Direct simulations of phase-change and phase-ordering phenomena are becoming more common. Recently qualitative simulations of boiling phenomena have been undertaken by a large number of research groups. One seldom discussed limitations is that large values of gravitational forcing are required to simulate the detachment and rising of bubbles formed at a bottom surface. The forces are typically so large that neglecting the effects of varying pressure in the system becomes questionable. In this paper we examine the effect of large pressure variations induced by gravity using pseudopotential lattice Boltzmann simulations. These pressure variations lead to height dependent conditions for phase co-existence and nucleation of either gas or liquid domains. Because these effects have not previously been studied in the context of these simulation methods we focus here on the phase-stability in a one dimensional system, rather than the additional complexity of bubble or droplet dynamics. Even in this simple case we find that the different forms of gravitational forces employed in the literature lead to qualitatively different phenomena, leading to the conclusion that the effects of gravity induced pressure variations on phase-change phenomena should be very carefully considered when trying to advance boiling and cavitation as well as liquefaction simulations to become quantitative tools.

physics.flu-dyn↗

arXiv2022

Over-Relaxation in Diffusive Integer Lattice Gas

One of the most striking draw-backs of standard lattice gas methods over lattice Boltzmann methods is a much more limited range of transport parameters that can be achieved. It is common for lattice Boltzmann methods to use over-relaxation to achieve arbitrarily small transport parameters in the hydrodynamic equations. Here, we show that it is possible to implement over-relaxation for integer lattice gases. For simplicity we focus here on lattice gases for the diffusion equation. We demonstrate that adding a flipping operation to lattice gases results in a multi-relaxation time lattice Boltzmann scheme with over-relaxation in the Boltzmann limit.

physics.comp-ph↗

arXiv2021

Connecting lattice Boltzmann methods to physical reality by coarse-graining Molecular Dynamics simulations

The success of lattice Boltzmann methods has been attributed to their mesoscopic nature as a method derivable from a physically consistent microscopic model. Original lattice Boltzmann methods were Boltzmann averages of an underlying lattice gas. In the transition to modern lattice Boltzmann method, this link was broken, and the frequently used over-relaxation to achieve high Reynolds numbers has been seen as lacking physical motivation. While this approach has undeniable utility, it appeared to break the link to any underlying physical reality putting into question the special place of lattice Boltzmann methods among fluid simulation methods. In this letter, we show that over-relaxation arises naturally from physical lattice gases that are derived as a coarse-graining of Molecular Dynamics simulations thereby re-affirming the firm foundation of lattice Boltzmann methods in physical reality.

physics.comp-ph↗

arXiv2021

Shaping the equation of state to improve numerical accuracy and stability of the pseudopotential lattice Boltzmann method

Recently it was discovered that altering the shape of the meta stable and unstable branches of an equation of state (EOS) can greatly improve the numerical accuracy of liquid and gas densities in the pseudopotential method. Inspired by this approach we develop an improved approach that is benchmarked for both equilibrium and non-equilibrium situations. We show here that the original approach reduces the method stability in non-equilibrium situations. Here we propose a new procedure to replace the metastable and unstable regions of these EOS by alternative functions. Our approach does not affects the coexistence densities or the speed of sound of the liquid phase while maintaining continuity of the sound speed in the pressure-density curve. Using this approach we were able to reduce the relative error of the planar interface vapor density compared to the thermodynamic consistent value by increasing the vapor phase sound speed. To allow for the benchmarking of dynamic results we also developed a finite difference method (FD) that solves the same macroscopic conservation equation as the pseudopotential lattice Boltzmann method (LBM). With this FD scheme we are able to perform mesh refinement and obtain reference solutions for the dynamic tests. We observed excellent agreement between the FD solutions and our proposed scheme. We also performed a detailed study of the stability of the methods using simulations of a droplet impacting on a liquid film for reduced temperatures down to 0.35 with Reynolds number of 300. Our approach remains stable for a density ratio up to $3.38\cdot10^{4}$.

physics.flu-dyn↗

arXiv2021

Integer Lattice Gas with a sampling collision operator for the fluctuating Diffusion Equation

We developed an integer lattice gas method for the fluctuating diffusion equation. Such a method is unconditionally stable and able to recover the Poisson distribution for the microscopic densities. A key advance for integer lattice gases introduced in this paper is a new sampling collision operator that replaces particle collisions with sampling from an equilibrium distribution. This can increase the efficiency of our integer lattice gas by several orders of magnitude.

physics.flu-dyn↗

arXiv2021

Molecular dynamics lattice gas equilibrium distribution function for Lennard-Jones particles

The molecular dynamics lattice gas method maps a molecular dynamics simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method by taking a Boltzmann average over the molecular dynamics lattice gas. A key property of the lattice Boltzmann method is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the molecular dynamics simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient to describe the particle displacements in a broad transition regime between free particles and particles undergoing many collisions in one time step. In a recent publication, we proposed a Poisson weighted sum of Gaussians which shows better agreement with the molecular dynamics data. We derive a lattice Boltzmann equilibrium distribution function from the Poisson weighted sum of Gaussians model and compare it to a measured equilibrium distribution function from molecular dynamics data and to an analytical approximation of the equilibrium distribution function from a single Gaussian probability distribution function.

physics.comp-ph↗

arXiv2020

Momentum fluctuations in coarse grained systems

At first glance the definition of mass and momentum appears to be uniquely defined. We show here, however, that this certainty can be misleading for many coarse grained systems. We show that particularly the fluctuating properties of common definitions of momentum in coarse grained methods like lattice gas and lattice Boltzmann do not agree with a fundamental definition of momentum. In the case of lattice gases, the definition of momentum will even disagree in the limit of large wavelength. For short times we can give analytical representations for the distribution of different momentum measures and thereby give a full account of these differences.

cond-mat.stat-mech↗

arXiv2020

Non-Gaussian distribution of displacements for Lennard-Jones particles in equilibrium

Most meso-scale simulation methods assume Gaussian distributions of velocity-like quantities. These quantities are not true velocities, however, but rather time-averaged velocities or displacements of particles. We show that there is a large range of coarse-graining scales where the assumption of a Gaussian distribution of these displacements fails, and a more complex distribution is required to adequately express these distribution functions of displacements.

physics.comp-ph↗

arXiv2020

Force approach for the pseudopotential lattice Boltzmann method

The pseudopotential method is one of the most popular extensions of the lattice Boltzmann method (LBM) for phase change and multiphase flow simulation. One attractive feature of the original proposed method consists on its simplicity of adding a force dependent on a nearest-neighbor potential function, which became known as the Shan-Chen interaction force. Some of the well known drawbacks implied by this method involves lack of thermodynamic consistency and impossibility to control the surface tension independently. In order to correct these deficiencies, different approaches were developed in the literature, such as multirange interactions potential, which involves larger stencils than nearest-neighbor approach, and modified forcing schemes. In this work, a strategy is developed to control the liquid-gas density ratio and the surface tension by means of an appropriate interaction force field using only nearest-neighbor interactions. The proposed procedure is devised starting from the desired pressure tensor, which allow for the control of the equilibrium multiphase properties such as liquid-gas coexistence curve and surface tension. Then, it is shown how to derive an external force field able to replicate the effects of this pressure tensor in the macroscopic conservation equations. The final step of our procedure is implementing this external force in the LBE by using the classical Guo forcing scheme. Numerical tests regarding static and dynamic flow conditions were performed. Results obtained from simulations showed good agreement with expected analytical values. Most divergent solution observed was the droplet oscillation period under certain flow conditions, which deviated 9% from expected analytical result. The observed results corroborate that the proposed method is able to replicate the desired macroscopic multiphase behaviour.

physics.comp-ph↗

arXiv2020

Large fluctuations in non-ideal coarse-grained systems

Using the recently introduced Molecular Dynamics Lattice Gas (MDLG) approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon coarse-graining as is usually expected. These results suggest that current approaches to simulating fluctuating hydrodynamics may have to be augmented to achieve quantitative results for systems with a non-ideal equation of state. The MDLG method gives a guidance to the exact nature of the fluctuation in such systems.

physics.comp-ph↗

arXiv2019

Multicomponent Flow on Curved Surfaces: A Vielbein Lattice Boltzmann Approach

We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

physics.comp-ph↗

arXiv2019

Validity of the Molecular-Dynamics-Lattice-Gas Global Equilibrium Distribution Function

The MDLG method establishes a direct link between a lattice-gas method and the coarse-graining of a Molecular Dynamics approach. Due to its connection to Molecular Dynamics, the MDLG rigorously recovers the hydrodynamics and allows to validate the behavior of the lattice-gas or lattice-Boltzmann methods directly without using the standard kinetic theory approach. In this paper, we show that the analytical definition of the equilibrium distribution function remains valid even for very high volume fractions.

physics.comp-ph↗