Incompressible Lattice Boltzmann Research Articles

Micro Lubrication and Heat Transfer in Wedge-Shaped Channel Slider with Convex Surface Texture Based on Lattice Boltzmann Method

Hydrodynamic lubrication is widely used between two relatively moving objects, and the effect of fluid flow state and temperature distribution on lubrication performance in wedge-shaped gaps is a popular topic to study. In this paper, the incompressible double-distribution lattice Boltzmann method (LBM) is applied to study the effect of micro convex surface texture on micro lubrication and heat transfer in wedge-shaped channels. By comparing this model with the analytical solution of an infinitely wide wedge slider, the maximum pressure calculated by LBM is 0.1081 MPa, and the maximum pressure calculated by the Reynolds equation is 0.1079 MPa. The error of the maximum pressure is 1.11%, and the Reynolds equation result is slightly smaller. The reason is that the Reynolds equation ignores the influence of fluid inertia force on oil film pressure. The results indicate that the application of LBM can be used to study lubrication problems. Compared with the Reynolds equation, LBM can calculate the velocity field and pressure field in the film thickness direction, and can also observe precise flow field details such as vortices. Three micro convex texture shapes were established to study the effects of different convex textures on micro lubrication and oil film temperature distribution, and the velocity distribution, temperature distribution and oil film pressure along the oil film thickness direction were given. Under the same conditions, comparing the oil film pressure with and without surface texture, the results show that the maximum oil film pressure with surface texture 3 is increased by about 4.34% compared with that without surface texture. The slightly convex texture can increase the hydrodynamic lubrication effect and obtain greater load-bearing capacity, helping to reduce the possibility of contact friction. The results show that the convex surface texture can improve the hydrodynamic lubrication performance, increase the load carrying capacity and reduce the possibility of contact friction, and the convex surface texture can influence the temperature distribution of the oil film. At 3.6 mm in the slider length direction and 7.5 μm in the oil film thickness direction, the temperature of surface texture 1 is 402.64 K, the temperature of surface texture 2 is 403.31 K, and the temperature of surface texture 3 is 403.99 K. The presence of vortices is captured at a high convergence ratio.

Lattice Boltzmann method for studying the dynamics of a single rising bubble in shear-thickening power-law fluids

Bubble motion in non-Newtonian fluids is widespread in various industrial processes such as crude oil extraction, enhancement of boiling heat transfer, CO<sub>2</sub> sequestration and wastewater treatments. Systems containing non-Newtonian liquids, as opposed to Newtonian liquids, have shear-dependent viscosity, which can alter the hydrodynamic characteristics of the bubbles, such as their size, deformation, instability, terminal velocity, shear rate, and ultimately affect the bubble rising behaviors. In this work, The dynamic behavior of bubble rising in a shear-thickened fluid was studied using an incompressible lattice Boltzmann non-Newtonian gas-liquid two-phase flow model. The effects of the rheological exponent <i>n</i>, the Eötvös number (<i>Eo</i>), and the Galilei number (<i>Ga</i>) on the bubble deformation, terminal velocity, and the shear rate were investigated. The numerical results show that the degree of bubble deformation increases as <i>Eo</i> grows, and the effect of <i>n</i> on bubble deformation degree is correlated with <i>Ga</i>. On the other hand, the terminal velocity of the bubbles increases monotonically and nonlinearly with <i>Ga</i> for a given <i>Eo</i> and <i>n</i>, and the effect of <i>n</i> on the terminal velocity of the bubbles gets stronger as <i>Ga</i> increases. When <i>Ga</i> is fixed and small, the terminal velocity of the bubble increases and then decreases with the increase of <i>n</i> at small <i>Eo</i>, and increases with the increase of <i>n</i> when <i>Eo</i> is large; but when <i>Ga</i> is fixed and large, the terminal velocity of the bubble increases with the increase of <i>n</i> in a more uniform manner. In addition, regions with high shear rates can be found near the left and right ends of the bubble. The size of these regions increases as both <i>Eo</i> and <i>Ga</i>, and it first increases and then decreases as <i>n</i> increases. Finally, the orthogonal experimental method was used to obtain the impact of the aforementioned three factors on the shear rate and terminal velocity. For the shear rate, the order of influence is <i>n</i>, <i>Ga</i> and <i>Eo</i> in descending order. For the terminal velocity, <i>Ga</i> has the greatest influence, followed by <i>n</i>, and <i>Eo</i> has the least influence.

A fluid-structure interaction method for soft particle transport in curved microchannels

A numerical framework is presented to predict the transport of soft elastic capsules immersed in an incompressible fluid with the aim of simulating inertial microfluidics applications. The flow evolution is modeled by a fully incompressible lattice Boltzmann method whereas a finite element model is considered for describing the dynamics of deformable structures. An immersed boundary technique is adopted to reconstruct the solution in the vicinity of the immersed surface and the time integration of the fluid-structure interaction problem is obtained by following an explicit procedure. The effectiveness of the framework is validated by means of several test cases involving: flows between two parallel plates for Reynolds numbers in the range 1÷100; capsules immersed in a fluid at Stokes regime exhibiting small and large deformations under shear; capsules migrating in a long straight microchannel with square cross-section at low-to-moderate Reynolds number. A very good agreement between the present results and literature data obtained using different numerical methods is found for all test cases. Finally, the method allowed to accurately simulate incompressible flows subjected to large pressure difference between the inlet and the outlet, characteristic of long curved microchannels, obtaining very smooth particle dynamics.

Rectangular Cylinder Orientation and Aspect Ratio Impact on the Onset of Vortex Shedding

Rectangular cylinders have the potential to provide valuable insights into the behavior of fluids in a variety of real-world applications. Keeping this in mind, the current study compares the behavior of fluid flow around rectangular cylinders with an aspect ratio (AR) of 1:2 or 2:1 under the effect of the Reynolds number (Re). The incompressible lattice Boltzmann method is used for numerical computations. It is found that the flow characteristics are highly influenced by changes in the aspect ratio compared to the Reynolds number. The flow exhibits three different regimes: Regime I (steady flow), Regime II (initial steady flow that becomes unsteady afterward), and Regime III (completely unsteady flow). In the case of the cylinder with an aspect ratio of 2:1, vortex generation, variation in drag, and the lift coefficient occur much earlier at very low Reynolds numbers compared to the cylinder with an aspect ratio of 1:2. For the cylinder with an aspect ratio of 1:2, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 120, 121 ≤ Re ≤ 144, and 145 ≤ Re ≤ 200, respectively. For the cylinder with an aspect ratio of 2:1, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 24, 25 ≤ Re ≤ 39, and 40 ≤ Re ≤ 200, respectively. The cylinder with an aspect ratio of 1:2 is found to have the ability to stabilize the incoming flow due to its extended after-body flatness. Generally, it has been found that a cylinder with an AR of 2:1 is subjected to higher pressures, higher drag forces, higher curvatures of cross-flow rotations, and higher amplitudes of flow-induced drag, as well as higher lift coefficients and lower shedding frequencies, compared to cylinders with an AR of 1:2. In Regime III, elliptic and vertically mounted airfoil-like flow structures are also observed in the wake of the cylinders.

A simple and efficient parallel immersed boundary-lattice Boltzmann method for fully resolved simulations of incompressible settling suspensions

This study presents an efficient and parallel fully resolved direct numerical simulation (FR-DNS) of settling suspensions on multiple CPU cores based on the boundary-thickening direct forcing immersed boundary method (BTDF-IBM) and incompressible lattice Boltzmann method (LBM). The simple BTDF-IBM is used to meet the no-slip and no-penetration conditions on particle boundaries, and the incompressible LBM is used to achieve the capability of large pressure fluctuations in suspensions. In addition, a theoretical force model is used to compensate for the unresolved lubrication force between the two approaching particles. A swap strategy for the streaming step is used to reduce the memory storage of the LBM particle density functions to half. A distribution and communication strategy is proposed to handle the IBM computing and complete the immersed boundary (IB) force of the particles residing in the interface region between adjacent subdomains. The developed BTDF-IBM-LBM solver “PFlows” can simulate large particle-laden flows with more than O(106) particles and with a particle volume fraction of up to 0.4. An almost linear parallel speedup and efficiency of higher than 0.8 are obtained by testing three-dimensional (3D) cases (up to 1.0 billion fluid grids and 0.45 million particles) and two-dimensional (2D) cases (up to 1.2 billion fluid grids and 2.39 million particles). Finally, the framework is applied to three large-scale real simulations involving 50,000 particles settling in 2D and 3D bounded and unbounded domains for qualitative and quantitative validations. The particle settling behaviors and disturbed complex fluid flows in the vertical channel are demonstrated. The Boycott effect in the inclined channel is uncovered by a new mechanism that combines particle sliding at the lower sidewall with fluid convection in the upper region. The hindered settling of particles in the 3D periodic domain, which is affected by the strong particle-fluid hydrodynamic interactions and particle-particle many-body interactions at a high solid volume fraction, are analyzed. The complex behaviors and statistical characteristics of the suspensions are preliminarily revealed and analyzed, which demonstrates the prospective capability of the present framework for FR-DNS of large-scale 2D and 3D suspension flows that are relevant to many industrial applications by IB-LBM.

An approach combining the lattice Boltzmann method and Maxwell–Stefan equation for modeling multi-component diffusion

The lattice Boltzmann method is an appropriate mesoscopic-scale tool for investigating the diffusion processes. However, since the state-of-the-art multi-component diffusion lattice Boltzmann (LB) models are based on the kinetic theory and start from the lattice Bhatnagar–Gross–Krook model, some defects cannot be avoided: they are only suitable for steady flow and there are limitations for setting the velocity and viscosity in lattice units. We devise a new incompressible LB model for ideal gases in solid oxide fuel cells (SOFCs), which is based on the advection–diffusion equation and coupled with the Maxwell–Stefan (M–S) equation by relaxation time. The coupled M–S equation is used for correction, considering the driving force in a multi-component diffusion system. Our LB model is implemented to predict the concentration overpotentials of a porous anode in a SOFC. The overpotentials are calculated from an H2–H2O–Ar ternary mass transport simulation and compared to the corresponding experimental results and several published continuum-scale and LB computations, demonstrating that our model offers a better consistency with the experimental measurement. Moreover, a Stefan tube is simulated for benchmarking against the local parameters; this is compared with the related experimental data and demonstrates the accuracy of our LB model.

Numerical simulations of incompressible fluid flow in synthetic fractures using lattice Boltzmann method

The effect of the geometrical complexity on the fluid flow through single fractures is the subject of this study. Synthetic self-affine fractures with different waviness and local roughness are generated by SynFrac. Several fracture profiles were sliced from the generated fractures for 2D simulations. An incompressible lattice Boltzmann method with non-equilibrium extrapolation method was used to simulate the fluid flow through the generated rough fractures by solving the full Navier-Stokes equations. The results indicate that the scaling irregular nature has a great influence on the fluid flow through single fractures. The tortuosity and the randomly distributed stagnated areas had been confirmed as the reasons for the deviation from local cubic law both theoretically and numerically. The tortuosity tends to have a linear relationship with the standard deviations which represent the amplitude of the waviness on the large scale, and a second-order dependence on the fractal dimensions which presents the degree of local roughness. The recirculation zones were formed in the troughs of rough fractures even when the flow was a creeping one with the Reynolds number below 1. These stagnated areas were observed to have an intuitive influence on the local effective advective aperture. An effective volume ratio was defined to quantify this effect of eddies on the hydraulic aperture which had been related to the local roughness of the fractures. The tortuosity of the fluid flow and eddies formed along the fractures combined together to make the permeability deviate from the local cubic law.

Numerical research of the infinitely wide wedge flow based on the lattice Boltzmann method

A new computational fluid dynamics method, the incompressible lattice Boltzmann method (LBM) is utilized to simulate fluid flow of the infinitely wide wedge in this paper. Compared with the traditional method, LBM is a mesoscopic scale method and some characteristics can be described more clearly with LBM. In this article, three kinds of model .i.e. linear type, parabolic type and harmonic type wedge models are built. The streamline and velocity contour in the fluid field are described. The pressure distribution of different types wedge is studied in LBM. The results manifest that, for the same bottom boundary velocity, the parabolic type and harmonic type wedges are easy to form a vortex, and the load capacity in the harmonic type wedge model is the largest. This paper is ready to investigate the microscopic lubrication mechanism of journal bearing in the future.

Solid wall and open boundary conditions in hybrid recursive regularized lattice Boltzmann method for compressible flows

Complex geometries and open boundaries have been intensively studied in the nearly incompressible lattice Boltzmann method (LBM) framework. Therefore, only few boundary conditions for the high speed fully compressible LBM have been proposed. This paper deals with the definition of efficient boundary conditions for the compressible LBM methods, with the emphasis put on the newly proposed hybrid recursive regularized D3Q19 LBM (HRR-LBM) with applications to compressible aerodynamics. The straightforward simple extrapolation-based far-field boundary conditions, the characteristic boundary conditions, and the absorbing sponge layer approach are extended and estimated in the HRR-LBM for the choice of open boundaries. Moreover, a cut-cell type approach to handle the immersed solid is proposed to model both slip and no-slip wall boundary conditions with either isothermal or adiabatic behavior. The proposed implementations are assessed considering the simulation of (i) isentropic vortex convection with subsonic to supersonic inflow and outflow conditions, (ii) two-dimensional (2D) compressible mixing layer, (iii) steady inviscid transonic flow over a National Advisory Committee for Aeronautics (NACA) 0012 airfoil, (iv) unsteady viscous transonic flow over a NACA 0012 airfoil, and (v) three-dimensional (3D) transonic flows over a German Aerospace Center (DLR) F6 full aircraft configuration.

A generalized lattice Boltzmann model for fluid flow system and its application in two-phase flows

In this paper, a generalized lattice Boltzmann (LB) model with a source term in the continuity equation is proposed to solve both incompressible and nearly incompressible Navier–Stokes (N–S) equations. This model can be used to deal with single-phase and two-phase flows problems with a source term in the continuity equation. From this generalized model, we can not only get some existing models, but also derive new models. Moreover, for the incompressible model derived, a modified pressure scheme is introduced to calculate the pressure, and then to ensure the accuracy of the model. In this work, we will focus on a two-phase flow system, and in the frame work of our generalized LB model, a new phase-field-based LB model is developed for incompressible and quasi-incompressible two-phase flows. A series of numerical simulations of some classic physical problems, including a spinodal decomposition, a static droplet, a layered Poiseuille flow, and a bubble rising flow under buoyancy, are performed to validate the developed model. Besides, some comparisons with previous quasi-incompressible and incompressible LB models are also carried out, and the results show that the present model is accurate in the study of two-phase flows. Finally, we also conduct a comparison between quasi-incompressible and incompressible LB models for two-phase flow problems, and find that in some cases, the proposed quasi-incompressible LB model performs better than incompressible LB models.

Numerical investigation of various nanofluid heat transfers in microchannel under the effect of partial magnetic field: lattice Boltzmann approach

In the present paper, the effect of the external partial magnetic field is studied on the flow and heat transfer of various nanofluids in a microchannel via the incompressible preconditioned lattice Boltzmann method. The simulations are performed for various parameters such as Hartmann number (Ha) ranging from 0 to 40 and surface non-dimensional slip coefficient (B) of 0–0.03. The nanofluid volume fraction is fixed at 1%, and the results are compared with pure water. The effect of using different nanoparticles (Al2O3, CuO, Ag, and Fe) has been investigated on the Nusselt number. The acceptable results are obtained by comparing numerical and experimental data. The results generally show that using Ag and CuO nanoparticles, respectively, leads to the best and worst heat transfer rate. Eventually, the highest and lowest Nusselt numbers are from these nanoparticles, where Ag and Al2O3 give the worst and best stress rates. It is found that for a specific requirement of microchannels in heat transfer application, there would be a certain nanofluid by specific nanoparticles. This novel study opens discussion by proposing a new alternative way to improve the heat transfer in microchannel which is applicable to the systems where microchannel is used as heat sinks.

Simulation of flow and soot particle distribution in wall-flow DPF based on lattice Boltzmann method

A two-dimensional mesoscopic gas-solid two-phase flow model has been developed to investigate the flow and soot loading in the micro-channel of diesel particulate filters. Soot particle size examined is in the range of 10 nm–1 µm. The flow is solved by an incompressible lattice Boltzmann model and the transport of solid particles is described by the cell automation probabilistic model. The lattice Boltzmann-cell automation probabilistic model (LB-CA model) is validated with the results of previous studies. The effects of different upstream velocities on the flow field in channels are investigated. The distribution and deposition of soot particles with different sizes in clean channels are simulated based on the LB-CA method and the LB-Lagrangian method respectively. The effects of deposited soot particles on flow field are evaluated in real soot particle capture process. The results show that the distributions of velocity field and pressure field in the channel are significantly affected by the upstream velocity. Compared with the effect of the particle size, the upstream velocity is more influential on the particle deposition distributions. The profiles of deposition distribution from the LB-CA method are in close agreement with those from the LB-Lagrangian method. The deposition distributions of particles with different diameters at the top of the porous wall are similar to the distributions of wall velocity along the channel length. Generally, the deposited soot particles increase the axial pressure and decrease the axial velocity in the inlet channel. The evolution trend of the areas where wall velocity undergoes changes is consistent with that of the solid nodes made of the captured soot particles.

Lattice Boltzmann model of gas-liquid two-phase flow of incomprssible power-law fluid and its application in the displacement problem of porous media

A new incompressible gas-liquid two-phase flow model for non-Newtonian power-law fluid is proposed based on an incompressible lattice Boltzmann model. And the fundamental physical mechanism of Newtonian fluid displacing non-Newtonian power-law fluid liquid in porous medium is studied by using the proposed model. The effects of capillary number <i>Ca</i>, dynamic viscosity ratio <i>M</i>, surface wettability <i>θ</i>, porous medium geometry, and power law index <i>n</i> on the displacement process are investigated. The comprehensive results show that with the increase of capillary number, the displacement process turns faster, the fingering phenomenon becomes more obvious and the displacement efficiency decreases. However, for different values of power-law index <i>n</i>, the effects of the <i>Ca</i> on the displacement process have some differences. Specially, the decrease rate of displacement efficiency becomes slow if the displaced fluid is shear thickening fluid as compared with that if the displaced fluid is shear thinning fluid. On the other hand, the displacement efficiency decreases as dynamic viscosity ratio <i>M</i> increases. And the effect of the viscosity ratio on the displacement process becomes more obvious for the low value of the power-law index <i>n</i>. Moreover, the effect of the surface wettability of the porous medium on the displacement process is also related to the size of the power-law index. With the increase of the contact angle of the porous medium, the fingering phenomenon turns less obvious, and the displacement efficiency increases. However, with the increase of power-law index <i>n</i>, the influence of the contact angle on the displacement process decreases. Besides, the displacement processes with different geometric types of the porous media are also studied in the work. The results show that comparing with the case of porous medium denoted by circle shape and square shape, the fingering phenomenon obtained by the case of triangular shape is most obvious, and the displacement efficiency is lowest.

Investigation of MHD effect on nanofluid heat transfer in microchannels

An incompressible preconditioned lattice Boltzmann method (IPLBM) is proposed to investigate the fluid flow and heat transfer characteristics of nanofluid in microchannel with hydrophilic or superhydrophobic walls and partially under the influence of transverse magnetic field as well as a heat flux. The modified IPLBM is shown to overcome the velocity inaccuracy in developing regime under partial magnetic field with respect to standard LBM. Then, the method is utilized to resolve the velocity and temperature fields at Re = 100 and various volume fractions of nanoparticles (0 ≤ φ ≤ 0.2%), Hartmann numbers (0 ≤ Ha ≤ 30) and slip coefficients (0 ≤ B ≤ 0.1). Superhydrophobic walls are shown to reduce the wall shear stress at B = 0.1 of up to 38.4, 58.5 and 70%, respectively, for Ha = 0, 15 and 30. Ignoring the temperature jump in modeling overestimates the Nusselt number with an error that culminates at B = 0.1 and φ = 0.2% to 19.6, 22.7 and 25%, respectively, for Ha = 0, 15 and 30. It is concluded that with magnetic field presence and realistic temperature jump, the surface material of superhydrophobic walls should be chosen properly to avoid inevitable and uncontrolled reduction in heat transfer, such that the highest hydrophobicity is not always the best choice. Reasonable agreements are achieved by comparing our results with credible analytic and numerical solutions and also with an experimental study.

Hydrodynamic stability and turbulent transition with the Vreman LES SGS and a modified lattice Boltzmann equation

For the evaluation of a broad range of Re in incompressible flows, particularly unsteady and transition regimes, the Vreman subgrid scale model is studied within the framework of a modified lattice Boltzmann equation. A unique multiple relaxation time form which recovers the fully incompressible unsteady Navier-Stokes equations is derived for the D3Q19 lattice. Solutions to the 3D-driven cavity are compared to a number of lattice Boltzmann and Navier-Stokes solutions. Initial simulations demonstrate the vanishing nature of eddy viscosity in the steady laminar regime. Onset of unsteadiness is found between Re 1900 and 1950, matching well with the wealth of literature. At Re 6000, velocity history and complex vortex structures show a transition to turbulence near the domain bottom and front walls while the centre of the domain retains laminar characteristics. By Re 8000 intermittent turbulence has progressed to the domain centre. This range of Re for transition and the flow characteristics are in agreement with the general ranges in literature, with further observations being added here. The Vreman model with an incompressible lattice Boltzmann method is found to be a promising tool for laminarto- turbulent simulation.

Lattice Boltzmann simulation of melting in a cubical cavity with a local heat-flux source

A three-dimensional numerical study is conducted to investigate the effect of heat-flux source location on the melting of phase change material (PCM) in a cubical cavity. An enthalpy-based incompressible thermal lattice Boltzmann model (iTLBM) has been established and validated by two benchmark problems. In order to reveal the effect of heat-flux source location in melting rate in three-dimensional space, both horizontal and vertical locations are considered. The numerical results show that the size of local heater and its heat flux play an essential role in melting rate. Furthermore, the variation of the location of the heat-flux source from both sides to the middle region of the cavity leads to the increase of the total heat flux on the interface, which also results in the increase of melting rate. Finally, we also find that the melting rate increases as the location of the heat-flux source is changed from top to the bottom region of the cavity, which is attributed to the enhancement of convection heat transfer.

Phase-field lattice Boltzmann modeling of boiling using a sharp-interface energy solver.

The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system. The mass flow generated at liquid-vapor phase interface is embedded in the pressure evolution equation. The sharp-interface treatment of internal energy equation helps to find the interfacial mass flow rate accurately where no free parameter is needed in the calculations. The proposed model is verified against available theoretical solutions of the two-phase Stefan problem and the two-phase sucking interface problem, with which our simulation results are in good agreement. The liquid droplet evaporation in a superheated vapor, the vapor bubble growth in a superheated liquid, and the vapor bubble rising in a superheated liquid are analyzed and underlying physical characteristics are discussed in detail. The model is successfully tested for the liquid-vapor phase change with large density ratio up to 1000.

Transition Flow with an Incompressible Lattice Boltzmann Method

AbstractDirect numerical simulations of the transition process from steady laminar to chaotic flow are considered in this study with the relatively new incompressible lattice Boltzmann equation. Numerically, a multiple relaxation time fully incompressible lattice Boltzmann equation is implemented in a 2D driven cavity. Spatial discretization is 2nd-order accurate, and the Kolmogorov length scale estimation based on Reynolds number (Re) dictates grid resolution. Initial simulations show the method to be accurate for steady laminar flows, while higher Re simulations reveal periodic flow behavior consistent with an initial Hopf bifurcation at Re 7,988. Non-repeating flow behavior is observed in the phase space trajectories above Re 13,063, and is evidence of the transition to a chaotic flow regime. Finally, flows at Reynolds numbers above the chaotic transition point are simulated and found with statistical properties in good agreement with literature.

An Alternative Lattice Boltzmann Model for Incompressible Flows and its Stabilization

AbstractIn this paper, an alternative lattice Boltzmann (LB)model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretizedwith the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

A dynamically adaptive lattice Boltzmann method for thermal convection problems

AbstractUtilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103up to 105are compared with benchmark results.