Regularized Lattice Boltzmann Method Research Articles

A regularized lattice Boltzmann method based on the multi-layer grid using a buffer scheme

The regularized lattice Boltzmann method (RLBM) has the advantage of improving the accuracy of numerical simulations without increasing the computational overhead. The RLBM usually uses the standard Cartesian grid in numerical simulation. This paper introduces the multi-layer grid technique, the multi-layer grid has different resolutions, which is also more consistent with the physical laws of the flow field. Based on this, a multi-layer grid regularized lattice Boltzmann method (ML-RLBM) for solving complex flow problems is proposed. The proposed method performs local refinement of the grid on the standard Cartesian grid to achieve a multi-layer grid, which can reduce the computational overhead. In order to realize the local grid refinement easily, this paper adopts the center point format to store the multi-layer grid. The ML-RLBM designs a buffer scheme between different layers of grids, which realizes that only spatial interpolation is required at the interface of different layers of grids without temporal interpolation. The numerical results show that the ML-RLBM has excellent numerical accuracy and numerical stability, and it can effectively reduce the computational cost.

Cooling effects of the derived coolant-film layer from partitioned porous injectors for transpiration cooling

This study aims to reveal the cooling benefits of the derived coolant film from partitioned porous injectors for transpiration cooling. The near-wall flow development and the cooling performance are investigated based on various layouts of porous injectors. The numerical investigation is conducted using an in-house recursive regularized thermal lattice Boltzmann method (RR-TLBM). The validated RR-TLBM solver is accelerated by three Tesla V100 graphic processing units (GPUs) for the simulation of incompressible and coupled-domain transpiration cooling at high Reynolds numbers, based on high-resolution grids with 2.65 × 108 nodes. The results indicate that the near-wall flow shows high momentum with the partitioned porous injectors. And the mean velocity increases by more than 23 % with the same coolant consumption per unit blowing area, which contributes to the coolant-film development and cooling uniformity downstream. Moreover, the partitioned porous layout shows the possibilities of coolant reduction as compared to the single continuous porous injector in Case 1. A reduction of 43 % in total coolant consumption with the partitioned porous layout only results in a decrease of 6 % in cooling performance downstream. Additionally, the partitioned coolant injection improves local cooling performance by roughly 22 %, with better cooling homogeneity at the same total coolant consumption. Turbulent fluctuations are weakened in the partitioned coolant injection zones, which contributes to an improvement in cooling evenness. The partitioned porous layout can be an appropriate choice for transpiration cooling systems.

Macroscopic finite-difference scheme based on the mesoscopic regularized lattice-Boltzmann method.

In this paper, we develop a macroscopic finite-difference scheme from the mesoscopic regularized lattice Boltzmann (RLB) method to solve the Navier-Stokes equations(NSEs) and convection-diffusion equation(CDE). Unlike the commonly used RLB method based on the evolution of a set of distribution functions, this macroscopic finite-difference scheme is constructed based on the hydrodynamic variables of NSEs (density, momentum, and strain rate tensor) or macroscopic variables of CDE (concentration and flux), and thus shares low memory requirement and high computational efficiency. Based on an accuracy analysis, it is shown that, the same as the mesoscopic RLB method, the macroscopic finite-difference scheme also has a second-order accuracy in space. In addition, we would like to point out that compared with the RLB method and its equivalent macroscopic numerical scheme, the present macroscopic finite-difference scheme is much simpler and more efficient since it is only a two-level system with macroscopic variables. Finally, we perform some simulations of several benchmark problems, and find that the numerical results are not only in agreement with analytical solutions, but also consistent with the theoretical analysis.

Numerical Analysis of Non-Newtonian Fluid Effects on the Equilibrium Position of a Suspended Particle and Relative Viscosity in Two-Dimensional Flow

A solvent in suspension often has non-Newtonian properties. To date, in order to determine these properties, many constitutive equations have been suggested. In particular, power-law fluid, which describes both dilatant and pseudoplastic fluids, has been used in many previous studies because of its simplicity. Then, the Herschel–Bulkley model is used, which describes fluid with yield stress. In this study, we considered how a non-Newtonian solvent affected the equilibrium position of a particle and relative viscosity using the regularized lattice Boltzmann method for fluid and a two-way coupling scheme for the particle. We focused on these methods so as to evaluate the non-Newtonian effects of a solvent. The equilibrium position in Bingham fluid was closer to the wall than that in Newtonian or power-law fluid. In contrast, the tendency of relative viscosity in Bingham fluid for each position was similar to that in power-law fluid.

Large-Scale Cluster Parallel Strategy for Regularized Lattice Boltzmann Method with Sub-Grid Scale Model in Large Eddy Simulation

As an improved method of the lattice Boltzmann method (LBM), the regularized lattice Boltzmann method (RLBM) has been widely used to simulate fluid flow. For solving high Reynolds number problems, large eddy simulation (LES) and RLBM can be combined. The computation of fluid flow problems often requires a large number of computational grids and large-scale parallel clusters. Therefore, the high scalability parallel algorithm of RLBM with LES on a large-scale cluster has been proposed in this paper. The proposed parallel algorithm can solve complex flow problems with large-scale Cartesian grids and high Reynolds numbers. In order to achieve computational load balancing, the domain decomposition method (DDM) has been used in large-scale mesh generation. Three mesh generation strategies are adopted, namely 1D, 2D and 3D. Then, the buffer on the grid interface is introduced and the corresponding 1D, 2D and 3D parallel data exchange strategies are proposed. For the 3D lid-driven cavity flow and incompressible flow around a sphere under a high Reynolds number, the given parallel algorithm is analyzed in detail. Experimental results show that the proposed parallel algorithm has a high scalability and accuracy on hundreds of thousands of cores.

Numerical modeling of fluid–structure–piezoelectric interaction for energy harvesting

In the present work, we propose a numerical coupling scheme combining the corotational Finite Element Method (FEM) for solid beams, the regularized Lattice Boltzmann Method (LBM) for fluid flows and a PiezoElectric Model (PEM) for energy harvesting module. The proposed coupling method can be employed to numerically solve Fluid–Structure–PiezoElectric Interaction (FSPEI) multiphysics problems which are the fundamental phenomena in the considered energy harvesting applications. In the proposed coupling method, the FEM and LBM are strongly coupled through the implicit Immersed Boundary Method (IBM) ensuring exactly the no-slip condition. Comparing with volumetric FEMs, the adopted corotational beam formulation can not only allow for large structural displacements, but also help improve the computational efficiency, as the solid structures for energy harvesting devices are usually slender under large motion. The piezoelectric effects are incorporated into the corotational beam dynamics with the help of the virtual work principle. The FEM, LBM and PEM are coupled together in a strong way in the sense that the time integrations are carried out without staggered communications. The proposed coupling scheme is assessed by a series of validation test-cases with increasing complexity, in which a good agreement is obtained with references.

On application of the regularized lattice Boltzmann method for isothermal flows with non-vanishing Knudsen numbers

Despite the advances in microscale modelling capabilities, physically observed non-zero Knudsen number (Kn) effects still elude the lattice Boltzmann method (LBM). This article details various Regularized LBM (RLBM) strategies used to model microscale flows and presents a thorough analysis on their applicability for the force-driven Poiseuille flow problem. In particular, we compare the formulations of eight schemes: Projected RLBM (P-RLBM), standard and Galilean Invariant Filtered Collision RLBM, Kn-dependant P-RLBM, Recursively Regularized LBM (R-RLBM), Hybrid R-RLBM, Central-Moment RLBM, and Onsager-Regularized LBM. We demonstrate, at different Kn with discrete Maxwell’s diffuse kinetic wall boundary conditions, the numerical equivalence of the considered RLBM schemes for hard sphere molecules on the D2Q9 lattice. Thereafter, we include a Kn-dependant wall-modified mean-free-path and extend the characterization onto higher-order D2Q17, D2Q21 and Q2Q25-Zero-One-Three, Q2Q49-Zero-One-Two-Three lattices. The study indicates that RLBM schemes are Navier-Stokes solvers which fail to entirely capture all the non-equilibrium phenomenon of slip/transition regime flows.

Near-wall vortices and thermal simulation of coupled-domain transpiration cooling by a recursive regularized lattice Boltzmann method

The present study aims to reveal the near-wall vortices and the effects of flow states in coupled-domain transpiration cooling using a recursive regularized thermal lattice Boltzmann method (RR-TLBM). Large-eddy simulations of turbulent flow and heat transfer have been conducted on high-resolution computational grids using a desktop-level computer with CUDA 11.6. Results indicate that the near-wall flow structures present spatial characteristics along the streamwise direction. The vortex evolution promotes the downstream heat dissipation, even though turbulence impairs the effective cooling area. The spanwise evolvement of vortices strengthens the mixing of coolant and hot gas, and small-scale structures are beneficial for turbulent heat transfer. Moreover, the transition onset occurs earlier at higher Reynolds numbers, and it weakens the downstream cooling. The cooling performance of the derived coolant film is improved as the Reynolds number varies from 5 × 103 to 3 × 104 with a blowing ratio of F = 10%, whereas the local cooling is impaired at the high Reynolds numbers exceeding 5 × 104. The variation in flow states has little influence on the cooling performance at the Reynolds numbers larger than 3 × 106. On the other hand, our in-house RR-TLBM solver is highly stable and efficient for the simulation of flow and heat transfer with high Reynolds numbers. Simultaneously, a high computational performance of 1127 million lattices updated per second is achieved for our simulation of a coupled-domain turbulent flow and heat transfer, using the desktop-level computer with three Tesla V100 graphics processing units.

Comparative study of the virtual flux method and immersed boundary method coupled with regularized lattice Boltzmann method for suspension flow simulations

Suspension flows are ubiquitous in many fields, and reducing computational costs for numerical simulations of suspension flows remains a great challenge. Numerical simulations of particle-laden flows were performed here using the regularized lattice Boltzmann method (RLBM). RLBM, coupled with the virtual flux method (VFM) or the immersed boundary method (IBM) with the multi-direct forcing approach, conducted a series of three simulations for stationary and moving boundaries. The VFM and IBM results were compared for validation, and the computational efficiency was evaluated. For the two simulations using stationary and moving boundaries (i.e., a steady flow past a stationary cylinder and a plane Poiseuille flow including a single moving circular particle), the results based on the VFM and IBM were qualitatively comparable. The computational time for IBM was longer than that for VFM due to the iterations in its scheme. The pressure-driven suspension flow simulations showed that a dilute suspension's (<5%) relative viscosity was almost equivalent. The difference between the results obtained by the VFM and IBM in the semidilute regime (>10%) was discussed in terms of particle rotational motion. Even though the scalability for parallel computing was comparable between the VFM and IBM, the computational time could be effectively reduced by using the VFM instead of the IBM because of the increased suspension concentration.

Kinetic Slip Boundary Condition for Isothermal Rarefied Gas Flows Through Static Non-Planar Geometries Based on the Regularized Lattice-Boltzmann Method

Kinetic Slip Boundary Condition for Isothermal Rarefied Gas Flows Through Static Non-Planar Geometries Based on the Regularized Lattice-Boltzmann Method

Blade Dimension Optimization and Performance Analysis of the 2-D Ugrinsky Wind Turbine

With the increasing focus on renewable energy, there is a need to improve the efficiency of vertical-axis wind turbines (VAWTs). The Ugrinsky wind turbine is a type of VAWT, but there are few studies on this turbine. Previous studies have shown that the maximum power coefficient of the Ugrinsky wind turbine reaches 0.170, which is 54.5% higher than that of the Savonius type (0.110), and this turbine maintains a high power coefficient over a wide range of tip speed ratios (TSR). In this study, the dimensions of the two semicircles of the Ugrinsky wind turbine were further optimized to obtain a higher power coefficient. An analysis of the effect of the blade dimensions on the performance was conducted. The flow around the turbine was simulated using the regularized lattice Boltzmann method. The geometry of the turbine was simulated using the virtual flux method for the Cartesian grid. The optimization was conducted in terms of the output power coefficient and the average value of the power coefficient for neighboring TSR to consider the fluctuation of the TSR. This study demonstrates that a closer vortex distance favored the growth of the vortex and improved the power coefficient.

Propagation pattern for moment representation of the lattice Boltzmann method.

A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This paper extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.

Regularized lattice Boltzmann method parallel model on heterogeneous platforms

AbstractAs an improved method of lattice Boltzmann method (LBM), regularized lattice Boltzmann method (RLBM) has been applied to simulate fluid flow. Nevertheless, the performance of RLBM needs to be considered when simulating actual problems. The rise of multicore platforms, especially the popularity of graphics processor units (GPUs), has provided possible implementation solutions for parallel computing. In this article, an RLBM parallel model on the CPU/GPU heterogeneous platforms is proposed. To solve the problem of possible GPU memory shortage, the CPU controls the startup of the kernel function in the RLBM algorithm and participates in the calculation. Due to the characteristics of the algorithm, the entire flow field is divided into CPU computing areas and GPU computing areas according to the given flow field division rules. OpenMP and CUDA are, respectively, applied to CPU and GPU for parallel computing. The startup of the kernel function takes a short time, and the CPU and GPU can be approximately regarded as performing calculations simultaneously. Since the data exchange between the CPU and GPU has a significant impact on performance, a buffer is set at the boundary of the CPU and GPU to reduce the frequency of data exchange. The buffer size determines the number of program iterations before exchanging data. The performance of the algorithm is measured by MFLUPS, and the algorithm is applied to the 3D lid‐driven cavity flow. The obtained results show that the MFLUPS of the algorithm is 25 times that of CPU MFLUPS, and it adds an increment equivalent to CPU MFLUPS compared with GPU MFLUPS. And the algorithm is extended to a multi‐GPU version, which is also applied to the 3D lid‐driven cavity flow. The results obtained show that the MFLUPS of the multi‐GPU version is 1.8 times that of the single GPU.

Onsager-regularized lattice Boltzmann method: A nonequilibrium thermodynamics-based regularized lattice Boltzmann method.

The regularized class of lattice Boltzmann methods (LBMs) leverage the potency of the standard lattice-Bhatnagar-Gross-Krook method by filtering out spurious nonhydrodynamic moments from the moment space; this is achieved through evaluating regularized populations via a multiscale or a Hermite polynomial expansion approach. In this paper, we propose an alternative approach for evaluating the lattice populations. This approach is based on a kinetic theory that is consistent with nonequilibrium thermodynamics and obeys the Onsager-reciprocity principle. The proposed method is verified and validated for a number of canonical problems such as the athermal shock tube, the double periodic shear layer, the lid driven cavity, flow past square cylinder, and Poiseuille flow at nonvanishing Knudsen numbers. Additionally, the proposed method is compared to existing regularized LBM schemes and is shown to yield significant improvement in the stability and accuracy of the simulations.

Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows

Rheological properties of the suspension flow, especially effective viscosity, partly depend on spatial arrangement and motion of suspended particles. It is important to consider effective viscosity from the microscopic point of view. For elliptical particles, the equilibrium position of inertial migration in confined state is unclear, and there are few studies on the relationship between dynamics of suspended particles and induced local effective viscosity distribution. Contribution of a single circular or elliptical particle flowing between parallel plates to the effective viscosity was studied, focusing on the particle–wall distance and particle rotational motion using the two-dimensional regularized lattice Boltzmann method and virtual flux method. As a result, confinement effects of the elliptical particle on the equilibrium position of inertial migration were summarized using three definitions of confinement. In addition, the effects of particle shape (aspect ratio and confinement) on the effective viscosity were assessed focusing on the particle–wall distance. The contribution of particle shape to the effective viscosity was found to be enhanced when the particle flowed near the wall. Focusing on the spatial and temporal variation of relative viscosity evaluated from wall shear stress, it was found that the spatial variation of the local relative viscosity was larger than temporal variation regardless of the aspect ratio and particle–wall distance.

Grid refinement in the three-dimensional hybrid recursive regularized lattice Boltzmann method for compressible aerodynamics.

Grid refinement techniques are of paramount importance for computational fluid dynamics approaches relying on the use of Cartesian grids. This is especially true of solvers dedicated to aerodynamics, in which the capture of thin shear layers require the use of small cells. In this paper, a three-dimensional grid refinement technique is developed within the framework of hybrid recursive regularized lattice Boltzmann method (HRR-LBM) for compressible high-speed flows, which is an efficient collide-stream-type method on a compact D3Q19 stencil. The proposed method is successfully assessed considering several test cases, namely, an isentropic vortex propagating through transition interface, shock-vortex interaction with intersection between grid refinement interface and shock corrugation, and transonic flows over three-dimensional DLR-M6 wing with seven levels of grid refinement.

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.

Pseudoentropic derivation of the regularized lattice Boltzmann method.

The lattice Boltzmann method (LBM) facilitates efficient simulations of fluid turbulence based on advection and collision of local particle distribution functions. To ensure stable simulations on underresolved grids, the collision operator must prevent drastic deviations from local equilibrium. This can be achieved by various methods, such as the multirelaxation time, entropic, quasiequilibrium, regularized, and cumulant schemes. Complementing a part of a unified theoretical framework of these schemes, the present work presents a derivation of the regularized lattice Boltzmann method (RLBM), which follows a recently introduced entropic multirelaxation time LBM by Karlin, Bösch, and Chikatamarla (KBC). It is shown that both methods can be derived by locally maximizing a quadratic Taylor expansion of the entropy function. While KBC expands around the local equilibrium distribution, the RLBM is recovered by expanding entropy around a global equilibrium. Numerical tests were performed to elucidate the role of pseudoentropy maximization in these models. Simulations of a two-dimensional shear layer show that the RLBM successfully reproduces the largest eddies even on a 16×16 grid, while the conventional LBM becomes unstable for grid resolutions of 128×128 and lower. The RLBM suppresses spurious vortices more effectively than KBC. In contrast, simulations of the three-dimensional Taylor-Green and Kida vortices show that KBC performs better in resolving small scale vortices, outperforming the RLBM by a factor of 1.8 in terms of the effective Reynolds number.

On the coupling of a direct-forcing immersed boundary method and the regularized lattice Boltzmann method for fluid-structure interaction

The present paper provides an analysis of the force model effect on the regularization procedure based on the Hermite expansion in regularized lattice Boltzmann method (RLBM). It is shown that, when using the 2nd-order accurate in time semi-implicit force model of Guo et al. [15] in RLBM, the reconstruction of the non-equilibrium part of the distribution function has to start from the 1st-order Hermite polynomial, because the new distribution function (after a change of variables) contains the body force effect. Based on this Hermite regularization, an immersed boundary-regularized lattice Boltzmann (IB-RLB) coupling method is proposed for simulating transient fluid-structure interactions (FSI) with rigid and deformable solid objects. The fluid and solid solvers are coupled in a non-staggered way so that the stability and accuracy are well preserved. The proposed IB-RLB coupling method is then validated with several numerical test-cases, such as impulsively started plate, vortex-induced vibrations and 3D flapping flag, for which good agreements are found with the references.

Pore scale characteristics of gas flow in shale matrix determined by the regularized lattice Boltzmann method

The flow mechanism of natural gas in the shale matrix is closely related to the high efficient development of shale gas reservoirs. However, the flow characteristic of shale gas in nanometer pores is scale dependent, and is also affected by the formation condition, adsorption layer, residual water saturation and detailed pore structure. In this study, a lattice Boltzmann model with a regularization procedure was applied to simulate shale gas flow in a 2D porous medium, and the effects of slippage, adsorption layer, residual water saturation and surface area on the apparent permeability were discussed. Simulation results indicate that the apparent permeability decreases with the increasing formation pressure, and increases with the increasing formation temperature and characteristic pore size. The adsorption layer and residual water affect the apparent permeability by changing the effective pore space for gas flow. And the effect is more obvious under the large Knudsen number conditions. When the porosity of the porous media is constant, the apparent permeability decreases with the increasing surface area, and the large surface area would even offset the positive effect of slippage on the apparent permeability.