Hybrid Lattice Boltzmann Method Research Articles

Hybrid lattice Boltzmann method using Cartesian and body-fitted grids for turbomachinery aeroacoustic simulations

In this study, we developed a hybrid approach using the lattice Boltzmann method (LBM) and finite-volume lattice Boltzmann method (FVLBM) to perform efficient aeroacoustic simulations with moving boundaries. An entire domain, including the flow and acoustic fields, was computed using the standard LBM with a Cartesian grid. Local domains around the moving objects were computed using the FVLBM with body-fitted grids. These simulations were coupled using the direct forcing method to consider moving boundaries. The hybrid method was validated for several problems including turbulent flows and flow-induced sounds under low-Mach-number conditions. These validation problems covered flows with Reynolds numbers up to 2.0×105 and Mach numbers less than 0.2. In the simulations of the aeolian tone generated from stationary and rotating cylinders, the hybrid method results were consistent with those of the conventional methods. In the simulation of the turbulent flow and broadband sound of the isolated airfoil, the hybrid method was 15 times faster than the standard LBM and produced results consistent with the experimental results. Furthermore, the application of a cross-flow fan demonstrated that the hybrid method successfully simulated the flow and acoustic fields around the rotor.

A hybrid lattice Boltzmann method for gaseous detonations

This article is dedicated to the construction of a robust and accurate numerical scheme based on the lattice Boltzmann method (LBM) for simulations of gaseous detonations. This objective is achieved through careful construction of a fully conservative hybrid lattice Boltzmann scheme tailored for multi-species reactive flows. The core concept is to retain LBM low dissipation properties for acoustic and vortical modes by using the collide and stream algorithm for the particle distribution function, while transporting entropic and species modes via a specifically designed finite-volume scheme. The proposed method is first evaluated on common academic cases, demonstrating its ability to accurately simulate multi-species compressible and reactive flows with discontinuities: the convection of inert species, a Sod shock tube with two ideal gases and a steady one-dimensional inviscid detonation wave. Subsequently, the potential of this novel approach is demonstrated in one- and two-dimensional inviscid unsteady gaseous detonations, highlighting its ability to accurately recover detonation structures and associated instabilities for high activation energies. To the authors' knowledge, this study is the first successful simulation of detonation cellular structures capitalizing on the LBM collide and stream algorithm.

Hybrid-lattice Boltzmann Method for the Simulation of Magnetohydrodynamic Conjugate Heat Transfer and Entropy Generation in Three Dimensions

Hybrid-lattice Boltzmann Method for the Simulation of Magnetohydrodynamic Conjugate Heat Transfer and Entropy Generation in Three Dimensions

Review of Lattice Boltzmann Method Applied to Computational Aeroacoustics

This paper presents the research studies carried out on the application of lattice Boltzmann method (LBM) to computational aeroacoustics (CAA). The Navier-Stokes equation-based solver faces the difficulty of computational efficiency when it has to satisfy the high-order of accuracy and spectral resolution. LBM shows its capabilities in direct and indirect noise computations with superior space-time resolution. The combination of LBM with turbulence models also work very well for practical engineering machinery noise. The hybrid LBM decouples the discretization of physical space from the discretization of moment space, resulting in flexible mesh and adjustable time-marching. Moreover, new solving strategies and acoustic models are developed to further promote the application of LBM to CAA.

Three-Dimensional Simulation of Heat and Mass Transfer by the Hybrid Lattice Boltzmann Method

Three-Dimensional Simulation of Heat and Mass Transfer by the Hybrid Lattice Boltzmann Method

Numerical analysis of self-driven temperature-sensitive magnetic fluid heat flow around two side-by-side heating cylinders under a solenoidal magnetic field

A temperature-sensitive magnetic fluid (TSMF) is a functional fluid that enables heat transfer due to the temperature difference and magnetic field. Using this property, we can increase the driving force while promoting heat transfer by increasing the heat transfer area, in the same manner as a heat sink. However, when multiple cylinders are juxtaposed, the interference between the cylinders will greatly affect the heat transfer. In the present study, we used the hybrid lattice Boltzmann method to investigate the flow and heat transfer characteristics of a TSMF around two side-by-side heating circular cylinders under a solenoidal magnetic field. As the magnetic field increases, the heat transfer effect increases. Moreover, when the distance between the cylinders is close enough, the heat flow becomes unstable. Under the same magnetic field conditions, the unstable flow can promote heat transfer.

Assessment of high order regularized hybrid lattice Boltzmann scheme for turbulent thermal convection

In this paper, fluid behavior and the second order statistics of developed turbulent natural convection is numerically predicted by the hybrid lattice Boltzmann method. In order to simulate the high Rayleigh number flow, the high order regularized lattice Boltzmann scheme combined with the finite difference solution of energy equation is used. An in-house code was carefully validated against the reference data computed by different numerical macroscopic and mesoscopic techniques. Simulations were performed for cavity aspect ratio 1 ≤ Ar ≤ 4 and Rayleigh number 1010 ≤ Ra ≤ 1011. It was found that two-dimensional (2D) models overpredicted turbulent statistics in comparison with three-dimensional (3D) models. Moreover, less stratified thermal fields are observed under 2D simulations. However, the mean Nusselt numbers are well agreed both for 2D and 3D models. The proposed hybrid model with uniform grid spacing reproduced integral heat transfer characteristics with acceptable accuracy for engineering applications. In particular, the relative error in the mean Nusselt number is within 5% when comparing the results with conventional fully resolved Navier-Stokes formulation.

Large eddy simulation of a thermal impinging jet using the lattice Boltzmann method

A compressible Hybrid Lattice Boltzmann Method solver is used to perform a wall-resolved Large eddy simulation of an isothermal axisymmetric jet issuing from a pipe and impinging on a heated flat plate at a Reynolds number of 23 000, a Mach number of 0.1, and an impingement distance of two jet diameters. The jet flow field statistics, Nusselt number profile (including the secondary peak), and shear stress profile were well reproduced. The azimuthal coherence of the primary vortical structures was relatively low, leading to no discernible temporal periodicity of the azimuthally averaged Nusselt number at the location of the secondary peak. While local unsteady near-wall flow separation was observed in the wall jet, this flow separation did not exhibit azimuthal coherence and was not found to be the only cause of the thermal spots blue, which lead to the secondary peak in the Nusselt number, as stream-wise oriented structures also played a significant role in increasing the local heat transfer.

Restoring the conservativity of characteristic-based segregated models: Application to the hybrid lattice Boltzmann method

A general methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum, and energy equations are solved by different methods. It is especially designed here for developing new numerical discretizations of the total energy equation and adapted to a thermal coupling with the lattice Boltzmann method (LBM). The proposed methodology is based on a linear equivalence with standard discretizations of the entropy equation, which, as a characteristic variable of the Euler system, allows efficiently decoupling the energy equation with the LBM. To this extent, any LBM scheme is equivalently written under a finite-volume formulation involving fluxes, which are further included in the total energy equation as numerical corrections. The viscous heat production is implicitly considered thanks to the knowledge of the LBM momentum flux. Three models are subsequently derived: a first-order upwind, a Lax–Wendroff, and a third-order Godunov-type schemes. They are assessed on standard academic test cases: a Couette flow, entropy spot and vortex convections, a Sod shock tube, several two-dimensional Riemann problems, and a shock–vortex interaction. Three key features are then exhibited: (1) the models are conservative by construction, recovering correct jump relations across shock waves; (2) the stability and accuracy of entropy modes can be explicitly controlled; and (3) the low dissipation of the LBM for isentropic phenomena is preserved.

High-order methods for diffuse-interface models in compressible multi-medium flows: A review

The diffuse interface models, part of the family of the front capturing methods, provide an efficient and robust framework for the simulation of multi-species flows. They allow the integration of additional physical phenomena of increasing complexity while ensuring discrete conservation of mass, momentum, and energy. The main drawback brought by the adoption of these models consists of the interface smearing, increasing with the simulation time, therefore, requiring a counteraction through the introduction of sharpening terms and a careful selection of the discretization level. In recent years, the diffuse interface models have been solved using several numerical frameworks including finite volume, discontinuous Galerkin, and hybrid lattice Boltzmann method, in conjunction with shock and contact wave capturing schemes. The present review aims to present the recent advancements of high-order accuracy schemes with the capability of solving discontinuities without the introduction of numerical instabilities and to put them in perspective for the solution of multi-species flows with the diffuse interface method.

A linear stability analysis of compressible hybrid lattice Boltzmann methods

An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard lattice is proposed. In this framework, the mass and momentum equations are addressed using the lattice Boltzmann method (LBM), while finite difference (FD) schemes solve an energy equation. Both systems are coupled with each other thanks to an ideal gas equation of state. This work aims at answering some questions regarding the numerical stability of such models, which strongly depends on the choice of numerical parameters. To this extent, several one- and two-dimensional HLBM classes based on different energy variables, formulations (primitive or conservative), collision terms and numerical schemes are scrutinized. Once appropriate corrective terms introduced, it is shown that all continuous HLBM classes recover the Navier-Stokes-Fourier behavior in the linear approximation. However, striking differences arise between HLBM classes when their discrete counterparts are analyzed. Multiple instability mechanisms arising at relatively high Mach number are pointed out and two exhaustive stabilization strategies are introduced: (1) decreasing the time step by changing the reference temperature Tr and (2) introducing a controllable numerical dissipation σ via the collision operator. A complete parametric study reveals that only HLBM classes based on the primitive and conservative entropy equations are found usable for compressible applications. Finally, an innovative study of the macroscopic modal composition of the entropy classes is conducted. Through this study, two original phenomena, referred to as shear-to-entropy and entropy-to-shear transfers, are highlighted and confirmed on standard two-dimensional test cases.

Improved compressible hybrid lattice Boltzmann method on standard lattice for subsonic and supersonic flows

A D2Q9 Hybrid Lattice Boltzmann Method (HLBM) is proposed for the simulation of both compressible subsonic and supersonic flows. This HLBM is an extension of the model of Feng et al. [1], which has been found, via different test cases, to be unstable for supersonic regimes. To circumvent this limitation, we propose:: (1) a new discretization of the lattice closure correction term that makes possible the simulation of supersonic flows, (2) a corrected viscous stress tensor that takes into account polyatomic gases, and (3) a novel discretization of the viscous heat production term fitting with the regularized formalism. The result is a hybrid method that resolves the mass and momentum equations with an LBM algorithm, and resolves the entropy-based energy equation with a finite volume method. This approach fully recovers the physics of the Navier–Stokes–Fourier equations with the ideal gas equation of state, and is valid from subsonic to supersonic regimes. It is then successfully assessed with both smooth flows and flows involving shocks. The proposed model is shown to be an efficient, accurate, and robust alternative to classic Navier–Stokes methods for the simulation of compressible flows.

On the use of conservative formulation of energy equation in hybrid compressible lattice Boltzmann method

Effect of density variations on mass conservation properties is widely recognized in the lattice Boltzmann method (LBM), thus non-conservative form of scalar transport equation was commonly adopted within the framework of hybrid LBM. Focusing on the compressible hybrid LBM, mass conservation and its effect on energy conservation equation are studied in this paper. Starting from the analysis on mass conservation law recovered by LBM, the consistency between conservative and non-conservative formulations of energy conservation equation based on various thermodynamic variables and lattice Boltzmann equation is addressed. Driven by the theoretical analysis, a set of modified consistent energy equations in entropy and internal energy form is derived to reduce the error terms and improve the consistency. The theoretical analysis and modified energy equations are intensively evaluated by several numerical test cases, e.g., the isentropic vortex convection, three-dimensional compressible Taylor-Green vortex and shock-vortex interaction.

Toward fully conservative hybrid lattice Boltzmann methods for compressible flows

This article presents a new numerical scheme designed to solve for any scalar equation coupled with a lattice Boltzmann solver (in so-called hybrid methods). Its most direct application is solving an energy equation, in parallel with a lattice Boltzmann solver, dealing with mass and momentum conservation. The numerical scheme is specifically designed to compute the energy flux consistently with the mass and momentum flux (as is carried out, for instance, using Riemann solvers). This scheme effectively eliminates a major limitation of the current compressible hybrid lattice Boltzmann method, in which the energy conservation is tackled under a non-conservative form, leading to discretization errors on jump conditions across shocks. Combined with our recently presented pressure-based solver [G. Farag et al., “A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows,” Phys. Fluids 32(6), 066106 (2020)], the resulting hybrid lattice Boltzmann scheme is, to the authors’ knowledge, the first to numerically conserve mass, momentum, and total energy simultaneously.

Role of condensation on boiling heat transfer in a confined chamber

A theoretical model of the coupled boiling and condensation phase changer heat transfer in a confined chamber is developed and numerically analyzed based on the modified hybrid lattice Boltzmann method. The interaction of boiling and condensation behavior is investigated with particular attention focused on the influence of condensation surface wettability on the boiling heat transfer process. Besides, the temperature response and the detailed two-phase flow pattern inside the chamber with different condensation surface wettability are evaluated. The results indicated that an optimal contact angle of 85° for the condensation surface wettability promoted the heat transfer on the evaporation surface. Subsequently, two modified condensation surfaces (biphilic surface with alternative hydrophilic and hydrophobic regions and gradient surface with a gradual wettability transition from hydrophilic to hydrophobic) are proposed for further heat transfer enhancement of the confined chamber. The results of the boiling curves, the two-phase flow pattern and the local/averaged heat transfer coefficient on the evaporation surface indicated that, compared with the single wettability with the optimal contact angle, both modified condensation surfaces can achieve a higher critical heat flux and a higher boiling heat transfer coefficient. Among these, the biphilic surface can achieve relatively better heat transfer performance.

Lattice Boltzmann simulation of bubble evolution at boiling on surfaces with different wettability

The hybrid Lattice Boltzmann method is adopted for a detailed study of surface wettability effects on evolution of vapor bubbles and temperature field of heat exchange surface at boiling. The simulation results show that the bubble departure diameter increases with an increase of static contact angle, and its value normalized by the capillary length approaches 3 for superlyophobic surface. In the range of contact angles of 110° – 129° the size of the dry area bounded by triple contact line greatly increases compared to the bubble departure diameter. At contact angles θ ⩾ 153° the dry area does not shrink even at the bubble departure stage and the typical film boiling regime is observed. It has been shown that the deterioration of wettability affects the evolution of the temperature field beneath the bubble, which leads to a significant change in the local heat transfer rate.

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models.

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.

A fully coupled hybrid lattice Boltzmann and finite difference method-based study of transient electrokinetic flows.

Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability.

A Lattice-Boltzmann-based perturbation method

In this work, we report on the development and initial validation of a new hybrid numerical model for the simulation of incompressible flow. A kinetic Lattice Boltzmann method (LBM) model using a reduced domain is nested within an inviscid flow field to provide increased simulation fidelity where desired, while leveraging the computational efficiency of inviscid solutions. We formulate a fully (or strongly) coupled approach, in which a Helmholtz decomposition is applied to the flow, separating the inviscid and viscous perturbation parts. The latter component is driven by the inviscid field through nonlinear inviscid-perturbation interaction terms that, in conventional Navier-Stokes solvers, would be expressed as volume forces. In the present work an equivalent LBM approach is presented where, as opposed to a body-force coupling, a strong coupling within the LBM collision operators is presented. The resulting hybrid LBM is applied to validation cases for a wave driven boundary layer and the flow past a cylinder.

Nanofluid natural convection in a corrugated solar power plant using the hybrid LBM-TVD method

In the present study, the Buongiorno’s two-phase method was implemented to investigate the nanofluid heat transfer in a triangle solar collector with corrugated bottom wall. A novel hybrid Lattice Boltzmann method (LBM) with using Total Variation Diminishing (TVD) method was developed. The effects of important physical parameters such as Rayleigh number, volume fraction of nanoparticle and different types of corrugated walls on the fluid flow pattern, nanoparticles distribution and temperature fields are studied in details. Three cases were considered for the numerical simulation. It was found that the Case 2 has the largest heat transfer rate. Based on the obtained results, the center region (inside the enclosure) has nearly uniform particle distribution. However, the region near cold and hot wall have higher and lower nanoparticle concentration, respectively. With increasing nanofluid concentration (φ) while it is smaller than a critical value, the heat transfer enhancement’s ratio increases. In addition, when solid volume fraction of nanofluid is larger than the critical value, the heat transfer efficiency will be decreased by increasing the φ.