Lattice Boltzmann Equation Research Papers (original) (raw)

2025, Journal of Computational Physics

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.

2025

We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a modified equilibrium distribution in Maxwell-Boltzmann type. With the use of the rest particles and the particle reservoir, we were able to add one degree of freedom into the sound speed of the modeled fluid. When the sound speed is tuned small enough, the compressible region of fluid flow can be reached. An example 2-D model is presented, together with the numerical verification for its transport coefficients.

2025, Physical Review E

In this paper, a gas-kinetic Bhatnagar-Gross-Krook ͑BGK͒ model is constructed for the Rayleigh-Be ´nard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Prϭ1 in the original BGK model ͓P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 ͑1954͔͒. The two-dimensional Rayleigh-Be ´nard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results. ͓S1063-651X͑99͒00205-6͔

2025

In this paper, we proposed a combination of lattice Boltzmann method and finite different scheme to simulate an incompressible fluid flow problem. Our new model applies the constrained interpolated profile method to discretize the spatial gradient in the governing lattice Boltzmann equation. Compared with the conventional lattice Boltzmann scheme, the current scheme is more accurate. In addition, the proposed model requires less mesh size for the computational at various conditions compared to other lattice Boltzmann models. Simulation of lid-driven cavity flow whose Reynolds number up to 1000 were carried out in order to validate the proposed approach. Numerical results show excellent agreement with those obtained by the conventional computational fluid dynamics approaches.

2025, Physical Review E

The goal of this work is to advance the characteristics of existing lattice Boltzmann Dirichlet velocity boundary schemes in terms of the accuracy, locality, stability, and mass conservation for arbitrarily grid-inclined straight walls, curved surfaces, and narrow fluid gaps, for both creeping and inertial flow regimes. We reach this objective with two infinite-member boundary classes: (1) the single-node "Linear Plus" (LI + ) and (2) the two-node "Extended Multireflection" (EMR). The LI + unifies all directional rules relying on the linear combinations of up to three pre-or postcollision populations, including their "ghost-node" interpolations and adjustable nonequilibrium approximations. On this basis, we propose three groups of LI + nonequilibrium local corrections: (1) the LI + 1 is parametrized, meaning that its steady-state solution is physically consistent: the momentum accuracy is viscosity-independent in Stokes flow, and it is fixed by the Reynolds number (Re) in inertial flow; (2) the LI + 3 is parametrized, exact for arbitrary grid-rotated Poiseuille force-driven Stokes flow and thus most accurate in porous flow; and (3) the LI + 4 is parametrized, exact for pressure and inertial term gradients, and hence advantageous in very narrow porous gaps and at higher Reynolds range. The directional, two-relaxation-time collision operator plays a crucial role for all these features, but also for efficiency and robustness of the boundary schemes due to a proposed nonequilibrium linear stability criterion which reliably delineates their suitable coefficients and relaxation space. Our methodology allows one to improve any directional rule for Stokes or Navier-Stokes accuracy, but their parametrization is not guaranteed. In this context, the parametrized two-node EMR class enlarges the single-node schemes to match exactness in a grid-rotated linear Couette flow modeled with an equilibrium distribution designed for the Navier-Stokes equation (NSE). However, exactness of a grid-rotated Poiseuille NSE flow requires us to perform (1) the modification of the standard NSE term for exact bulk solvability and (2) the EMR extension towards the third neighbor node. A unique relaxation and equilibrium exact configuration for grid-rotated Poiseuille NSE flow allows us to classify the Galilean invariance characteristics of the boundary schemes without any bulk interference; in turn, its truncated solution suggests how, when increasing the Reynolds number, to avoid a deterioration of the mass-leakage rate and momentum accuracy due to a specific Reynolds scaling of the kinetic relaxation collision rate. The optimal schemes and strategies for creeping and inertial regimes are then singled out through a series of numerical tests, such as grid-rotated channels and rotated Couette flow with wall-normal injection, cylindrical porous array, and Couette flow between concentric cylinders, also comparing them against circular-shape fitted FEM solutions.

2025, Lecture Notes in Computer Science

We present a lattice gas model to simulate snow transport by wind and its deposition on a given ground pro le. Our approach is very well suited to a ne grained massively parallel computing.

2025, Lecture Notes in Computer Science

We consider two formulations of a cellular automata: the first one uses a gather-update paradigm and the second one a collisionpropagation paradigm. We show the equivalence of both descriptions and, using the latter paradigm, we propose a simple way to define a Cellular Automata on a graph with arbitrary topology. Finally, we exploit the duality of formulation to reconsider the problem of characterizing invertible cellular automata.

2025

Original Research Paper Received 10 August 2015 Accepted 30 October 2015 Available Online 05 December 2015 Numerous models have been proposed to incorporate various equations of state (EOS) into the pseudo potential model. This paper presents an investigation of different EOS types based on the Gong and Cheng model in multiphase-single component flows by the lattice Boltzmann method. Primarily, it is conducted to investigate eight EOS’s classified in four categories; the Shan-Chen EOS, the cubic EOS, the non-cubic EOS, and the cubic and non-cubic combination EOS. The results show that each EOS type results in producing relatively similar spurious currents and has a maximum achievable density ratio. Although by choosing a proper beta parameter for every EOS the simulation errors decrease dramatically, our results show it is impossible to set a constant parameter for the non-cubic EOS. Therefore, a new equation is introduced to predict an efficient beta for the cubic and the Shan-Chen...

2025, The Ramanujan Article

Without any formal education and extreme poverty conditions, ramanujan emerged as one of great mathematician of India. His mathematical ideas transformed and reshaped 20 century mathematics and their ideas are inspiration for 21 century mathematicians. His excellence can be realized from the fact that he discovered some results which are supposed to be true but have not been proved till date. His foresightedness was so scintillating that he gave those ideas in mathematics that no one can imagine to invent them.

2025, The Ramanujan Journal

2025

The lattice-Boltzmann method is a possible alternative to standard computational fluid dynamics (CFD) or direct simulation Monte Carlo (DSMC) simulations of fluid flows in continuum, slip and transition regimes. We evaluate the accuracy of the lattice-Boltzmann (LB) method for the simulation of microchannel fluid flows at finite Knudsen numbers. A novel modeling of the adaptive Knudsen number as a function of fluid density is proposed in the lattice-Boltzmann model. Specific boundary conditions are used to represent the slippage at the wall and for the simulation of open flows. We compare our simulation results with DSMC data.

2025

Grenoble INP Institut D'Ingénerie Master of Science CFD Modeling of Particle Migration in Viscoelastic Flows with Lattice-Boltzmann Method by Ahmed Hodaib Modeling of viscoelastic fluid flows is a growing concern and a challenging task. Having a quantitative understanding of viscoelastic suspensions is very important for industrial and biological concerns, such as petroleum industry, DNA analysis and drug transport in blood. These fluids are characterized by the memory effect, which is the fact that the deformation depends on the history of deformation, not only on the strain like Newtonian fluids. Lattice-Boltzmann method has been proved to be successful to model a wide range of physical problems. In this present work, Lattice-Boltzmann models are applied to simulate different two-dimensional benchmarks for viscoelastic fluid flows described by Oldroyd-B constitutive law. Then, the advection-diffusion scheme is coupled with the smoothed profile method to simulate the suspension of rigid particles. A MATLAB script is developed, and is validated with available analytical and experimental data for parabolic and shear flows for Newtonian and viscoelastic fluids. Then, simulations for fixed particles are done. Then, the code was used to simulate a single particle migration in viscoelastic shear flow, by computing the hydrodynamic forces and updating the particle position and velocity accordingly. It was found, as expected, that the particle migrates towards the closest wall, moving away from the centre of the channel in shear flow. Finally, the evolutions of the normal force, the transverse velocity, the angular velocity and the position of the particle are plotted with time.

2025, Physical Review E

In the present paper, we verify the effectiveness of the two-relaxation-time (TRT) collision operator in reducing boundary slip computed by the immersed boundary-lattice Boltzmann method (IB-LBM). In the linear collision operator of the TRT, we decompose the distribution function into symmetric and antisymmetric components and define the relaxation parameters for each part. The Chapman-Enskog expansion indicates that one relaxation time for the symmetric component is related to the kinematic viscosity. Rigorous analysis of the symmetric shear flows reveals that the relaxation time for the antisymmetric part controls the velocity gradient, the boundary velocity, and the boundary slip velocity computed by the IB-LBM. Simulation of the symmetric shear flows, the symmetric Poiseuille flows, and the cylindrical Couette flows indicates that the profiles of the numerical velocity calculated by the TRT collision operator under the IB-LBM framework exactly agree with those of the multi-relaxation time (MRT). The TRT is as effective in removing the boundary slip as the MRT. We demonstrate analytically and numerically that the error of the boundary velocity is caused by the smoothing technique using the delta function used in the interpolation method. In the simulation of the flow past a circular cylinder, the IB-LBM based on the implicit correction method with the TRT succeeds in preventing the flow penetration through the solid surface as well as unphysical velocity distortion. The drag coefficient, the wake length, and the separation points calculated by the present IB-LBM agree well with previous studies at Re = 10, 20, and 40.

2025, Transport in Porous Media

The development of focused ion beam-scanning electron microscopy (FIB-SEM) techniques has allowed high-resolution 3D imaging of nanometre-scale porous materials. These systems are of important interest to the oil and gas sector, as well as for the safe long-term storage of carbon and nuclear waste. This work focuses on validating the accurate representation of sample pore space in FIB-SEM-reconstructed volumes and the predicted permeability of these systems from subsequent single-phase flow simulations using a highly homogeneous nanometre-scale, mesoporous (2-50 nm) to macroporous (>50 nm), porous ceramic in initial developments for digital rock physics. The limited volume of investigation available from FIB-SEM has precluded direct quantitative validation of petrophysical parameters estimated from such studies on rock samples due to sample heterogeneity, large variations in recorded sample pore sizes and lack of pore connectivity. By using homogeneous synthetic ceramic samples we have shown that lattice-Boltzmann flow simulations using processed FIB-SEM images are capable of predicting the permeability of a homogeneous material dominated by 10-100 nanometre-scale pores (similar, albeit simpler, to those in natural samples) at the much larger scale where permeability measurements become practical. This result shows the LB flow simulations can be used with confidence in pores at this scale allowing future work to focus on sample preparation techniques for samples sensitive to drying and multiple FIB-SEM site selection for the population of larger-scale models for heterogeneous systems.

2025, Physical review

We propose a new way to implement Dirichlet boundary conditions for complex shapes using data from a single node only, in the context of the lattice Boltzmann method. The resulting novel method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well established Bouzidi et al. [1] boundary condition for curved walls, despite its local nature. The method also proves to be suitable to simulate moving rigid objects or immersed surfaces either with or without prescribed motion. The core idea of the new approach is to generalize the description of boundary conditions that combine bounce-back rule with interpolations and to enhance them by limiting the information involved in the interpolation to a close proximity of the boundary.

2025, The Journal of the Acoustical Society of America

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, which is of interest for aeroacoustic applications. Several solutions have been proposed but are often too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. An original regularized collision operator is proposed, based on the expansion of Hermite polynomials, that greatly improves the accuracy and stability of the LBM without significantly altering its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between this approach and both experimental and numerical data o...

2024

The scope of the paper is the simulation of the sound field radiated by a string in the time domain. Different time domain methods have been successfully implemented for string simulations. These methods not only perform real-time string sound synthesis, but also pressure and particle velocity generated near strings can be obtained. This is very useful to analyze sound field interaction with external physical structures, as well as body guitar, for example. In this paper, the use of a combination of timedomain methods to provide a complete and wider stable-in frequency range-description of sound field generated than classical finite differences approach is proposed. Functional Transformation Method (FTM) and Finite-Difference Time Domain (FDTD) Method supply different advantages, which used in a mixing scheme, give a wider broadband and efficient solution of sound field. Moreover, real-time modification of parameters without stability shortcomings is also feasible.

2024, Sustainability

Nuclear engineering requires computationally efficient methods to simulate different components and systems of plants. The Lattice Boltzmann Method (LBM), a numerical method with a mesoscopic approach to Computational Fluid Dynamic (CFD) derived from the Boltzmann equation and the Maxwell–Boltzmann distribution, can be an adequate option. The purpose of this paper is to present a review of the recent applications of the Lattice Boltzmann Method in nuclear engineering research. A systematic literature review using three databases (Web of Science, Scopus, and ScienceDirect) was done, and the items found were categorized by the main research topics into computational fluid dynamics and neutronic applications. The features of the problem addressed, the characteristics of the numerical method, and some relevant conclusions of each study are resumed and presented. A total of 45 items (25 for computational fluid dynamics applications and 20 for neutronics) was found on a wide range of nucl...

2024, Journal of Computational Physics

We propose a lattice Boltzmann method to treat moving boundary problems for solid objects moving in a fluid. The method is based on the simple bounce-back boundary scheme and interpolations. The proposed method is tested in two flows past an impulsively started cylinder moving in a channel in two dimensions: (a) the flow past an impulsively started cylinder moving in a transient Couette flow; and (b) the flow past an impulsively started cylinder moving in a channel flow at rest. We obtain satisfactory results and also verify the Galilean invariance of the lattice Boltzmann method.

2024, Computing in Science & Engineering

N a n o s c a l e C o m p u t i n g Multiscale Simulation of Nanobiological Flows A new multiscale approach for simulating nanobiological flows uses concurrent coupling of constrained molecular dynamics for long biomolecules with a mesoscopic lattice Boltzmann treatment of solvent hydrodynamics. The approach is based on a simple scheme of spacetime information exchange between the atomistic and mesoscopic scales.

2024

The three-dimensional thermal lattice Boltzmann-BGK model is developed to simulate the pressure-driven rarefied gaseous flow within a circular channel with constant-temperature-wall in the transition regime (0.1 <Kn<1). The D3Q15 model has been employed for velocity discretization. The captured nonlinear behavior of gas in the Knudsen layer, which dominates the flow characteristics in small-scale gaseous flows by modifying the near-wall correction function along with the variation of properties with density and temperature distributions are implemented in a new formulation. An appropriate combination of advanced straight boundary conditions and a 3D extension of an available curved boundary conditions by identifying the nodes either adjacent to the solid nodes or flow nodes on the computational domain with the structured mesh are employed. The results of small-scale phenomena such as slip-velocity and temperature-jump are reported, which are manifestations of the cases with non-zero Knudsen number. Due to the deficiency of the continuum presumption for high-Knudsen flows, the present study suggests that the TLBM is an efficient tool applicable to the theoretical development of low speed gas flow study, which typically falls within the realm of MEMS/ NEMS by virtue of its more straightforward boundary treatments and higher computation capability compared to other atomistic approaches.

2024

Ce travail de these sur les milieux poreux est axe sur deux parties. La premiere concerne l'etude numerique de l'ecoulement d'un fluide Newtonien ou non-Newtonien au sein d'un systeme fluide/poreux. L'approche a un seul domaine qui consiste a ecrire l'equation de Navier-Stokes incluant le terme de Darcy-Brinkman-Forchheimer est adoptee dans cette etude. La relation entre le gradient de pression et la vitesse debitante lineaire dans le cas de Darcy ou le fluide est Newtonien, est obtenue. Cette relation est etendue dans le cas non-Darcy ou le fluide est non Newtonien. L'influence des nombres de Darcy et de Forchheimer sur la structure de l'ecoulement est montree. Dans la seconde partie, une etude de stabilite lineaire et numerique de la convection naturelle de fluides viscoelastiques saturant une couche poreuse horizontale chauffee par un flux constant est realisee. Une etude d'instabilite primaire et secondaire nous a permis de montrer que pour un...

2024, Physical Review E

Rayleigh-Bénard convection is numerically simulated in two-and three-dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the advection-diffusion equation of a passive-scalar, is used to simulate the temperature field. A body force proportional to the temperature is applied, and the system satisfies the Boussinesq equation except for a slight compressibility. A no-slip, isothermal boundary condition is imposed in the vertical direction, and periodic boundary conditions are used in horizontal directions. The critical Rayleigh number for the onset of the Rayleigh-Bénard convection agrees with the theoretical prediction. As the Rayleigh number is increased higher, the steady two-dimensional convection rolls become unstable. The wavy instability and aperiodic motion observed, as well as the Nusselt number as a function of the Rayleigh number, are in good agreement with experimental observations and theoretical predictions. The LBE model is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer.

2024, Physical Review E

Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is found to have correct diffusion behavior and the multiple diffusion coefficients are obtained analytically. The analytical results are further confirmed by numerical simulations in a few solvable limiting cases. The LBE model is established as a useful computational tool for the simulation of mass transfer in fluid systems with external forces.

2024

We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of state and can undergo a liquid-gas type phase transition. The model is shown to be momentum-conserving. From the microscopic mechanical stability condition, the densities in bulk liquid and gas phases are obtained as functions of a temperature-like parameter. Comparisons with the thermodynamic theory of phase transition show that the LBE model can be made to correspond exactly to an isothermal process. The density profile in the liquid-gas interface is also obtained as function of the temperature-like parameter and is shown to be isotropic. The surface tension, which can be changed independently, is calculated. The analytical conclusions are verified

2024, Physical Review Letters

We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a BGK collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers. Higher order approximations to the Boltzmann equation can be achieved by using more velocities in the quadrature.

2024

This work was performed in part at Sandia National Laboratories, a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the US Department of Energy, contract DE-AC04-94AL85000.

2024, Physical Review E

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum-exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second-order accuracy based on our recent works ͓Mei et al., J. Comput. Phys. 155, 307 ͑1999͒; ibid. 161, 680 ͑2000͔͒. The stressintegration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: ͑i͒ two-dimensional pressure-driven channel flow; ͑ii͒ two-dimensional uniform flow past a column of cylinders; ͑iii͒ two-dimensional flow past a cylinder asymmetrically placed in a channel ͑with vortex shedding͒; ͑iv͒ three-dimensional pressure-driven flow in a circular pipe; and ͑v͒ threedimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

2024, HAL (Le Centre pour la Communication Scientifique Directe)

-Ces dernières années, l'intérêt pour l'IRM de flux 4D s'est accru pour sa capacitéà imager l'anatomie du coeur et la vitesse 3D du flux sanguin au cours du cycle cardiaque. Toutefois, les contraintes de l'application clinique nécessitent une acquisition avec une résolution limitée qui engendrent des difficultés pour la quantification de biomarqueurs hémodynamiques d'intérêt. Dans ce travail, nous proposons une solution originale pour améliorer la résolution de la carte de vitesse qui s'affranchie de la connaissance a priori du domaine fluide. Ainsi, notre approche s'appuie sur la résolution d'un problème inverse par minimisation d'un critère composé de trois termes : un terme de fidélité aux données, un terme s'appuyant sur la mécanique des fluides et un terme de lissage spatial. Dans cetteétude, nous présentons les résultats de validation obtenus sur un jeu de données synthétiques et une application clinique.

2024, International Journal for Numerical Methods in Fluids

A generic, mass conservative local grid reÿnement technique for the lattice-Boltzmann method (LBM) is proposed. As a volumetric description of the lattice-Boltzmann equation is applied, mass conservation can be imposed by allowing the lattice-Boltzmann particles to move from coarse grid cells to ÿne grid cells and vice versa in the propagation step. In contrast to most existing techniques, no spatial and temporal interpolation of particle densities is applied. Moreover, since the communication between the coarse and the ÿne grids is independent on the collision step, the method can be used for any LBM scheme. It was found that the method is second-order accurate in space for 2-D Poiseuille ow and di erent grid setups. The method was also applied to the case of 2-D lid driven cavity ow at Re = 1000, where half of the cavity was locally reÿned. It was found that the locations of the two lower vortices could be captured accurately. Finally, a direct numerical simulation (DNS) of turbulent channel ow at Re = 360 was performed where the grid was locally reÿned near the walls of the channel. Good ÿrst-and second-order turbulence statistics were obtained, showing the applicability of the local grid reÿnement technique for complex ows. Copyright ? 2005 John Wiley & Sons, Ltd.

2024, Transport in Porous Media

2024, Advances in Engineering Software

A 3D model for the numerical simulation of artificial aortic prostheses is presented, considering fluid-structure interaction. The method is based in the General Lattice Boltzmann equation under a multi-relaxation scheme. Streamlines, velocities and shear stresses inside the biological fluid are reported and discussed. Technical details of the algorithm are also described. As well, an algorithm for the LB mesh generation is presented and evaluated. Numerical results of artificial heart valves in aortic position are reported here, showing the versatility of the proposed approach.

2024, Afrique Science: Revue Internationale des Sciences et Technologie

La méthode de Lattice Boltzmann (LBM), des Différences Finies Explicites (DFE), Hybride combinant les deux méthodes précédentes et la méthode des Eléments finis (EF) sont utilisées afin de simuler la convection naturelle se développant dans une cavité de section droite carrée, contenant de l'air. Deux parois opposées sont à la température T c et les deux autres à T f avec T c > T f . La cavité est inclinée de 45° par rapport à l'horizontal. Les équations de transfert et les conditions aux limites sont adimensionnalisées et discrétisées. Une série de simulations est faite pour différentes valeurs du nombre de Rayleigh, c'est à dire pour différentes valeurs de l'écart de température entre les parois chaudes et les parois froides. L'analyse comparative des différentes méthodes montre que, pour les faibles nombres de Rayleigh, leurs performances sont à peu près les mêmes. Lorsque ce nombre augmente, la méthode LBM exige un maillage très fin du domaine d'étude, donc un temps de calcul beaucoup plus long. Par ailleurs, les simulations faites à l'aide des quatre méthodes ont toutes montré que pour Ra = 10 5 le régime est oscillant amorti, il est oscillant périodique à un nombre de Rayleigh Ra = 2.10 5 et chaotique à un nombre de Rayleigh Ra = 1,2.10 6 . Le principal avantage de la méthode LBM par rapport aux autres réside dans la simplicité de sa mise en oeuvre.

2024

We demonstrate how to produce a stable multispeed lattice Boltzmann method (LBM) for a wide range of velocity sets, many of which were previously thought to be intrinsically unstable. We use non-Gauss-Hermitian cubatures. The method operates stably for almost zero viscosity, has secondorder accuracy, suppresses typical spurious oscillation (only a modest Gibbs effect is present) and introduces no artificial viscosity. There is almost no computational cost for this innovation. DISCLAIMER: Additional tests and wide discussion of this preprint show that the claimed property of coupled steps: no artificial dissipation and the second-order accuracy of the method are valid only on sufficiently fine grids. For coarse grids the higher-order terms destroy coupling of steps and additional dissipation appears. The equations are true.

2024

Les equations de Navier-Stockes en leur forme complete sont tres compliquees du fait de la presence des termes non lineaires. La resolution de ces equations exige des hypotheses specifiques pour chaque situation. Dans cette contribution, on essayera d’etudier l’ecoulement non stationnaire d’un fluide incompressible dans un domaine cartesien en presence d’un gradient de pression. L’etude portera sur l’effet du temps et du gradient de pression sur l’evolution de la vitesse d’ecoulement. Pour resoudre le probleme, les methodes analytiques et numeriques seront utilisees.

2024, Zeitschrift für Naturforschung A

Although a variational iteration algorithm was proposed by Yildirim (Math. Prob. Eng. 2008 (2008), Article ID 869614) that successfully solves differential-difference equations, the method involves some repeated and unnecessary iterations in each step. An alternative iteration algorithm (variational iteration algorithm-II) is constructed in this paper that overcomes this shortcoming and promises to provide a universal mathematical tool for many differential-difference equations.

2024

Numerical solutions of 2-D laminar flow over a backwardfacing step using the lattice Boltzmann equation method (LBEM) are presented in this article. Unlike conventional numerical schemes based on macroscopic continuum equation (mass conservation and Navier-Stokes) discretisation, the LBEM is based on microscopic models and mesoscopic kinetic equations. The simulations were validated for a wide range of Reynolds numbers (100 ≤ Re ≤ 1,000), comparing them to previous studies. Several flow features, such as primary and secondary vortex location at the bottom and top of the wall, respectively, were investigated regarding Reynolds number. Two typical classes of boundary condition were implemented in the LBEM model: the Drichlet condition at the inlet flow (parabolic speed profile) and the Newman condition at the outlet flow (zero gradient speed). The results showed that the LBEM gave accurate results over a wide range of Reynolds number; these were compared with other numerical methods and experimental data.

2024, Journal of Computational Physics

2024, PAMM

The Lattice Boltzmann equations are usually constructed to satisfy physical requirements like Galilean invariance and isotropy as well as to possess a velocity‐independent pressure, no compressible effects, just to mention a few. In this paper, a stability criterion for such constructions is introduced and is used to derive a new relation of the parameters in a parametrized 2‐dimensional 9‐velocity model.

2024, Computational & Applied Mathematics

The treatment of control problems governed by systems of conservation laws poses serious challenges for analysis and numerical simulations. This is due mainly to shock waves that occur in the solution of nonlinear systems of conservation laws. In this article, the problem of the control of Euler flows in gas dynamics is considered. Numerically, two semi-linear approximations of the Euler equations are compared for the purpose of a gradient-based algorithm for optimization. One is the Lattice-Boltzmann method in one spatial dimension and five velocities (D1Q5 model) and the other is the relaxation method. An adjoint method is used. Good results are obtained even in the case where the solution contains discontinuities such as shock waves or contact discontinuities.

2024, Physical Review E

We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal values of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered... more

2024

Transport de contaminant dans un milieu poreux -- Les équations de base -- Solution numérique -- Schéma non oscillatoire avec évaluation exacte du front -- Étude numérique des transferts bidimensionnels dans la zone non saturée, application à l'étude du drainage et de la recharge d'une nappe à surface libre -- Modélisation de la migration d'un contaminant dense dans un milieu poreux saturé -- Transport d'un panache à plusieurs éléments contaminants dans un écoulement à densité variable -- Modélisation de la migration de contaminant dans le site d'enfouissement Borden en Ontario -- Champs d'application de la méthode EPCOF

2024, Physical Review A

A new method is presented for solving the space-independent Boltzmann-Enskog equation describing the motions of a heavy tagged particle (A) in the medium of light bath particles (B). It is shown how in the case of inverse-power-law repulsive interactions the transport equation can be transformed into a set of partial differential equations which are then solved successively to give the conditional average of an arbitrary physical quantity as a power series in the mass ratio 0 = m~l(mz +m&). The method is explicitly developed to first order in 0,whi ch shows the effects of fluctuations, and in the linear noise approximation the time-dependent distribution function itself is obtained. The velocity autocorrelation function of a tagged particle is evaluated to order Q where one finds corrections to a single exponential decay.

2024, Journal of Thermal Analysis and Calorimetry

Mixed convection heat and mass transfer of a hybrid nanofluid in a lid-driven irregular hexagon cavity is numerically studied in this paper. The nanofluid is composed of the multi-walled carbon nanotube and the magnesium oxide (MgO) nanoparticles (15-85 vol%) dispersed in a non-Newtonian carboxymethyl cellulose-based fluid obeying the Ostwald-de Waele rheological model. The governing equations are solved numerically by means of the finite volume method and the SIMPLER algorithm to treat the velocity-pressure coupling. The study is performed for some relevant physical parameters: the Richardson number (Ri = 0.001-10), the power law index (n = 0.2-1.0), the buoyancy ratio (N = − 3 to + 3), and the total solid volume fraction (φ = 0.0-0.02). The obtained results are presented in terms of streamlines, isotherms, isoconcentrations, velocity profiles, and local and average Nusselt and Sherwood numbers. This work proves the significant impact of the quoted parameters on the hydrodynamic, thermal, and mass fields. Indeed, the flow structure is more sensitive to the power law index and the Richardson number variations. Moreover, heat and mass transfer are enhanced by the decline of the latter. Also, the addition of nanoparticles enhances heat transfer for the three convection modes especially for the dominant forced convection mode (Ri = 0.001) where the improvement reaches 14.42% for a power law index equal to 0.8. However, it improves mass transfer in the dominant forced convection but in mixed and dominant natural convection (Ri = 1, 10) as the buoyancy ratio equal to + 2 and + 3. Keywords Mixed convection • Thermosolutal • Lid-driven irregular hexagon cavity • MWCNT-MgO/CMC non-Newtonian hybrid nanofluid • Finite volume method List of symbols c p Heat capacity (J kg −1 K −1) C Concentration (kg m −3) D Mass diffusivity (m 2 s −1) g Gravitational acceleration (m s −2) Gr Grashof number k Thermal conductivity (W m −1 K −1) K Consistency coefficient (Pa s n) L Length of the cavity (m) Le Lewis number n Power law index N Buoyancy ratio Nu Nusselt number Nu avg Average Nusselt number p Pressure (Pa) P Dimensionless pressure Pr Prandtl number Re Reynolds number Ri Richardson number S Dimensionless coordinate adopted for distance along the inclined walls Sh Sherwood number Sh avg Average Sherwood number T Temperature (K) u, v Velocity components (m s −1) U, V Dimensionless velocity components x, y Cartesian coordinates (m) X, Y Dimensionless Cartesian coordinates Greek letters α Thermal diffusivity (m 2 s −1) β Thermal expansion coefficient (K −1) Shear rate (s −1)

2024, Physics Letters A

A two-dimensional double Multiple Relaxation Time-Thermal Lattice Boltzmann Equation (2-MRT-TLBE) method is developed for predicting convective flows in a square differentially heated cavity filled with air (Pr = 0.71). In this Letter, we propose a numerical scheme to solve the flow and the temperature fields using the MRT-D2Q9 model and the MRT-D2Q5 model, respectively. Thus, the main objective of this study is to show the effectiveness of such model to predict thermodynamics for heat transfer. This model is validated by the numerical simulations of the 2-D convective square cavity flow. Excellent agreements are obtained between numerical predictions. These results demonstrate the accuracy and the effectiveness of the proposed methodology.

2024, Heat and Mass Transfer

The present paper deals with the numerical investigation of a 2D laminar fluid flow and heat transfer in a plane channel with two square blocks located at arbitrary positions. The numerical model is based on a coupling between the multiple relaxation time-lattice Boltzmann equation and the finite difference method for incompressible flow. Both the horizontal and the vertical separation distances between the two blocks are varied. Particular attention was paid to the distribution patterns of the time averaged local Nusselt number on the top and bottom walls. Results obtained from the present study show a complex flow patterns developed in the channel due to the change of the square blocks positions.

2024, Bulletin of the American Physical Society

Lattice Boltzmann Method for Interfacial Flows with High Density Ratio JIANGHUI CHAO, YANXIA ZHAO, RENWEI MEI, WEI SHYY, University of Florida -A computational model using Lattice Boltzmann Equation (LBE) method for two-phase flow with sharp interface and high density ratio is developed. The Lattice Boltzmann scheme simulates incompressible two-phase flow by solving two distribution functions simultaneously. The interfacial dynamics are modeled by incorporating the intermolecular interaction force (He et al., JCP, pp642-663, 1999). By using a new surface tension formulation to eliminate oscillations in surface tension profile, numerical stability is significantly improved. Sharp interface can be maintained for flows with density ratio at O( 2 ) or higher with little oscillation in velocity and pressure across interface. The detailed numerical assessment on the performance of the scheme based on the simulations of static bubble and rising bubble will be presented. The motion of a droplet on a wall is also studied using this improved method. The wetting boundary conditions on the wall are implemented to minimize the total free energy of the system. The motion of contact line, the contact angle, the surface tension, the velocity field and the pressure distribution are analyzed.

2024, Progress in Computational Fluid Dynamics

The method of lattice Boltzmann equation (LBE) is a kineticbased approach for fluid flow computations. In LBE, the distribution functions on various boundaries are often derived approximately. In this paper, the pressure interaction between an inlet boundary and the interior of the flow field is analysed when the bounce-back condition is specified at the inlet. It is shown that this treatment reflects most of the pressure waves back into the flow field and results in a poor convergence towards the steady state or a noisy flow field. An improved open boundary condition is developed to reduce the inlet interaction. Test results show that the new treatment greatly reduces the interaction and improves the computational stability and the quality of the flow field.

2024, Physical Review E

2024, Progress in Computational Fluid Dynamics, An International Journal