Lattice Boltzmann Flux Solver Research Articles

Flow-Induced Transverse Vibration of Three Equal-Diameter Cylinders in an Equilateral Triangle Using the Immersed Boundary–Lattice Boltzmann Flux Solver

Flow-Induced Transverse Vibration of Three Equal-Diameter Cylinders in an Equilateral Triangle Using the Immersed Boundary–Lattice Boltzmann Flux Solver

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

Expression of Concern: Parametric study on a convective flow in a thermal storage using IBM/thermal lattice Boltzmann flux solver

Expression of Concern: Parametric study on a convective flow in a thermal storage using IBM/thermal lattice Boltzmann flux solver

Implicit lattice Boltzmann flux solver: A novel mesoscopic numerical algorithm for geothermal reservoir simulation

In this work, a novel implicit lattice Boltzmann flux solver (LBFS) for simulating geothermal reservoirs is developed. LBFS is a mesoscopic approach that uses the reconstructed lattice Boltzmann model to calculate fluxes on the cell interface, which has a more solid physics foundation. Compared with macroscopic methods that directly use mathematical approximations, the dynamic changes of pressure and temperature in a reservoir can be simulated more accurately with LBFS. Therefore, in the present work, LBFS is introduced into geothermal reservoir simulation for the first time, and a fully implicit temporal discretization was realized by using the proposed dummy scalar triplet method to assemble the sparse matrix. This means that the adopted time step can far exceed the limitation of the Courant-Friedrichs-Lewy condition. Several test cases are implemented to validate the present algorithm, including the Theis problem, one-dimensional fluid flow and heat transfer, and two-dimensional radial fluid flow and heat transfer in aquifers. Finally, a production-reinjection doublet system was simulated by using an unstructured mesh. All of the obtained results agree well with the corresponding analytical solutions.

On the investigation of shock wave/boundary layer interaction with a high-order scheme based on lattice Boltzmann flux solver

Shock wave/boundary layer interaction (SWBLI) continues to pose a significant challenge in the field of aerospace engineering. This paper aims to address this issue by proposing a novel approach for predicting aerodynamic coefficients and heat transfer in viscous supersonic and hypersonic flows using a high-order flux reconstruction technique. Currently, finite volume methods are extensively employed for the computation of skin aerodynamic coefficients and heat transfer. Nevertheless, these numerical methods exhibit considerable susceptibility to a range of factors, including the inviscid flux function and the computational mesh. The application of high-order flux reconstruction techniques offers promising potential in alleviating these challenges. In contrast to other high-order methods, the flux reconstruction is combined with the lattice Boltzmann flux solver in this study. The current method evaluates the common inviscid flux at the cell interface by locally reconstructing the lattice Boltzmann equation solution from macroscopic flow variables at solution points. Consequently, this framework performs a positivity-preserving, entropy-based adaptive filtering method for shock capturing. The present approach is validated by simulating the double Mach reflection, and then simulating some typical viscous problems. The results demonstrate that the current method accurately predicts aerodynamic coefficients and heat transfer, providing valuable insights into the application of high-order methods for shock wave/boundary layer interaction.

An improved multiphase lattice Boltzmann flux solver with a modified Cahn–Hilliard equation for multiphase flow with super large density ratio

In this study, a modified Cahn–Hilliard equation with a very simple format was proposed, which can be used to simulate immiscible multi-component/multiphase flow with a super large density ratio. In addition, based on this modified equation and the Navier–Stokes equations, an improved multiphase lattice Boltzmann flux solver (IMLBFS) has been proposed, and its computational ability has been tested by multiple numerical examples, including Laplace law, two bubbles merging, contact angle, bubble rising, and droplet splashing on a thin film. The results show that the proposed IMLBFS can simulate immiscible two-phase flow with a very large density ratio up to 1:5000 or 1:10 000 under various operating conditions, including the Reynolds number reaching 10 000. In addition, IMLBFS also has excellent features such as clear physical properties, freely adjustable source term strength, and effective suppression of mass loss.

An improved axisymmetric interfacial lattice Boltzmann flux solver for large-density-ratio multiphase flows

In this paper, an improved axisymmetric interfacial lattice Boltzmann flux solver abandoning the previous predictor-corrector scheme is proposed. Unlike the previous model starting from the two-dimensional standard lattice Boltzmann method (LBM), the present method is developed using the axisymmetric LBM, which directly incorporates the axisymmetric effects into the distribution functions. As a result, the proposed solver does not need the corrector step involving complicated space derivatives. It makes this method simpler and more computationally efficient. In the present solver, the resultant governing equation is globally resolved by the finite volume method, while the fluxes are reconstructed by local application of the axisymmetric LBM. Therefore, the inconsistency between the local reconstruction and the global governing equation can be eliminated because the global equation can be strictly derived from the axisymmetric LBM, which holds stronger physical basis than the previous method. Numerical experiments about the interface capturing and the multiphase flows are conducted to test the proposed model. Results show that the present method is superior to the fractional step solver in terms of the accuracy, stability, and computational efficiency. In addition, this solver has the capacity of simulating large-density-ratio and complex interfacial change.

Multiphase lattice Boltzmann flux solver with conservative Allen‐Cahn model for modeling high‐density‐ratio flows

AbstractIn this paper, the Allen‐Cahn‐Multiphase lattice Boltzmann flux solver (AC‐MLBFS) is proposed as a new and effective numerical simulation method for multiphase flows with high density ratios. The MLBFS resolves the macroscopic governing equations with the finite volume method and reconstructs numerical fluxes on the cell interface from local solutions to the lattice Boltzmann equation, which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann methods for simulating incompressible multiphase flows while alleviating their limitations. Previous MLBFS‐based multiphase solvers performed poorly in mass conservation, which might be caused by the excessive numerical diffusion in the Cahn‐Hilliard (CH) model used as the interface tracking algorithm. To resolve this problem, the present method proposes using the conservative Allen‐Cahn (AC) model as the interfacial tracking algorithm, which can ease the numerical implementation by removing high order derivative terms and alleviate mass leakage by enforcing local mass conservation in the physical model. Numerical validations will be carried out through benchmark tests at high density ratios and in extreme conditions with large Reynolds or Weber numbers. Through these examples, the accuracy and robustness as well as the mass conservation characteristics of the proposed method are demonstrated.

Implementation and Validation of Explicit Immersed Boundary Method and Lattice Boltzmann Flux Solver in OpenFOAM

In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems.

A consistent generalized model-based lattice Boltzmann flux solver for incompressible porous flows

The recently developed lattice Boltzmann flux solver (PLBFS) for the incompressible porous flow is free from the limitations of coupled streaming time step and the mesh spacing, and the uniform meshes and the complex distribution function treatment at the boundary. However, the local flux reconstruction is inconsistent with the global governing equations in PLBFS. To overcome the drawback, a consistent generalized lattice Boltzmann flux solver for the incompressible porous flow is proposed based on the generalized lattice Boltzmann method (GLBM). The recovered macroscopic governing equations given by the Chapman–Enskog analysis of GLBM are globally resolved by the finite volume method. Specifically, the macroscopic variables are updated at cell centers using the three-step Runge–Kutta method, while the solution of the GLBM is locally applied for the fluxes reconstruction at cell interfaces. Unlike the PLBFS, the forcing term can be naturally incorporated into the interface fluxes reconstruction, which gives the present method a stronger physical basis and ensures global consistency. Moreover, different from the PLBFS, the streaming time step used at the cell interface is decoupled from the updating time step at the cell center in the present solver. Furthermore, a simplified flux reconstruction strategy is proposed to avoid complex calculations and save computing resources. Several numerical examples have been adopted to test the proposed method. The simulations of the nonlinear lid-driven cavity flow show that our method is more accurate than the original PLBFS. Results also demonstrate that the simplified method can reduce the computational time by 43%.

Investigations of spray breakup Rayleigh–Taylor instability via multiphase lattice Boltzmann flux solver

Poor fuel–air mixing of the diesel spray in low ambient temperature and pressure or thin air leads to intricate fuel breakup mechanism near the nozzle, which still remains worth of study. In this study, a pressure-based modified multiphase lattice Boltzmann flux solver (MLBFS) is proposed to accommodate the fuel spray breakup characteristics of multiphase, multicomponent, and large density ratio, in which the source terms of governing equation are modified emphatically for high injection pressure. Therefore, the characteristics of microscopic diesel spray breakup induced by Rayleigh–Taylor instability are investigated, including spray penetration, spray area, and spray arc length. It is revealed that the spray penetration is increased exponentially with the fuel–air density ratio Rρ. Influenced by air resistance and circulation interference, the roll-up vortex, droplet size, and spray area increase with the decreasing of Rρ (corresponding to high ambient pressure). Affected by entrainment and Rayleigh–Taylor instability, the development of the spray arc length experienced three stages: rapid growth, peak, and violent fluctuation, in which the lower Rρ facilitates development. It is concluded that Rayleigh–Taylor instability is favorable for stimulating the spray internal circulation of spray to enhance entrainment with surrounding air, while improving roll-up and breakup in the spray tail region. Such investigation is conductive to better understanding the micro-breakup mechanisms of fuel spray in the spray-induced internal combustion engine.

An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.

An implicit immersed boundary method for Robin boundary condition

In this work, a novel boundary condition-enforced immersed boundary method (IBM) for simulating complex thermal–fluid–structure interaction (TFSI) problems with Robin boundary conditions is proposed. In this work, two auxiliary layers of Lagrangian points are introduced and placed within the inner and outer parts of the immersed object to enable the simultaneous evaluation of the temperature and its gradient on the solid surface. The mutual thermal interactions between the immersed object and the surrounding flow are taken into account through the temperature corrections on the Lagrangian points by accurately enforcing the Robin boundary condition on the solid boundary. Hence, a system of linear equations can be formulated to compute the temperature corrections. Subsequently, the temperature corrections are biasedly distributed to the Eulerian points located in the inner auxiliary layer to eliminate the diffusion generated by the smooth delta function on the temperature field outside the solid object. The proposed IBM integrated with the reconstructed thermal lattice Boltzmann flux solver (RTLBFS) is extensively and critically assessed with classical benchmark cases ranging from two-dimensional stationary problems to three-dimensional problems involving moving boundaries to demonstrate the robustness and accuracy of the proposed method for Robin boundary conditions. Results from the present work are extensively corroborated with previous works that adopt different approaches for imposing the Robin boundary condition. It shows that the proposed method not only provides a much more accurate representation of the Robin boundary condition but also introduces a simple implementation for the complex Robin boundary condition within the diffuse interface IBM framework.

A three-dimensional high-order flux reconstruction lattice boltzmann flux solver for incompressible laminar and turbulent flows

A three-dimensional (3D) high-order flux reconstruction lattice Boltzmann flux solver (FR-LBFS) is developed in this paper for accurate and efficient simulations of incompressible laminar and turbulent flows. The original lattice Boltzmann flux solver (LBFS) is a second-order finite volume method (FVM) which combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. But it is not convenient to construct high-order FVM, and the compactness is always a bottleneck. The present work separates LBFS from FVM and combines LBFS with high-order FR scheme. Thus, the FR-LBFS inherits the superiority of LBFS and FR and shares the following attractive features: (i) a fully-explicit arbitrary order compact method, (ii) weakly compressible (WC) model for unsteady incompressible flows and (iii) evaluating inviscid and viscous fluxes simultaneously and no particular technique requirement, such as local discontinuous Galerkin method (LDG), for viscous term discretization. To validate the current method, various 3D incompressible laminar isothermal and thermal numerical experiments are presented first. Good agreements are achieved between the current results and the previous experimental and numerical data whilst the present high-order solver adopt coarse meshes. Furthermore, the ability of the proposed method to perform accurate and stable computations of incompressible decaying homogeneous isotropic turbulent flows and turbulent channel flows with different mesh resolutions and accuracy orders are investigated. The results show that the present 3D FR-LBFS is a promising tool for under-resolved or implicit large eddy simulation (ILES) of incompressible turbulent flows.

Development of three-dimensional rotated lattice Boltzmann flux solver for the simulation of high-speed compressible flows

A three-dimensional (3D) Rotated Lattice Boltzmann Flux Solver (RLBFS) is proposed and analyzed with matrix-based linear stability theory for simulating compressible flows in a wide range of Mach numbers. The 3D RLBFS applies the finite volume method to discrete the Navier-Stokes equations and evaluates its fluxes at each cell interface. To improve numerical stability, the convective fluxes are obtained in a hybrid way by using the D1Q4 lattice Boltzmann model in two perpendicular directions decomposed by the outer normal vector of each cell interface. The viscous fluxes are computed in a conventional way using the second-order central scheme. The stability performance and order accuracy of the proposed 3D RLBFS are examined by using the matrix-based stability theory and L2 errors on different meshes respectively. It is shown that the 3D RLBFS is stable even at high Mach number and has the second-order accuracy in space. The reliability and capability of the proposed method is further evaluated by simulating several challenging compressible flow problems, including subsonic flow over the DLR-F4, transonic flow over the ONERA M6 wing, supersonic flow around NACA0012 wing, hypersonic flow over the Viking lander capsule, hypersonic flow over a hemisphere and hypersonic flow around a blunt nose double cone. The obtained numerical results are in good agreement with experimental and/or numerical data published in the literature, indicating that the present method provides a reliable and effective tool for simulating practical three-dimensional compressible flow problems in aeronautics and astronautics.

General mechanisms for stabilizing weakly compressible models.

Many weakly compressible models with intrinsic mechanisms for stabilizing computation have been proposed to simulate incompressible flows. The present paper analyzes several weakly compressible models to establish general mechanisms that incorporate them into a unified and simple framework. It is found that all these models contain some identical numerical dissipation terms, mass diffusion terms in the continuity equation, and bulk viscosity terms in the momentum equation. They are proven to provide general mechanisms for stabilizing computation. Referring to the general mechanisms and the computational procedures of the lattice Boltzmann flux solver, two general weakly compressible solvers for isothermal flows and thermal flows are proposed. They can be directly derived from standard governing equations and implicitly introduce those numerical dissipation terms. Detailed numerical investigations demonstrate that the two general weakly compressible solvers have good numerical stability and accuracy for both isothermal and thermal flows, which validates the general mechanisms further and the general approach of constructing general weakly compressible solvers.

Development of a Moving-Least-Square-based Immersed Boundary Method for the simulation of viscous Compressible Flows

In this paper, a Moving-Least-Squares (MLS)-based immersed boundary method (IBM) for simulating viscous compressible flows is proposed. For this method, the compressible lattice Boltzmann flux solver (LBFS) is used to solve the flow field on the Eulerian mesh and the MLS-based IBM introduced in present paper is used to implement boundary condition. The discrete Lagrangian points are used to represent the Solid boundaries. A second-order MLS interpolation is used for numerical exchange between two grids of IBM. The forced implicit boundary condition is adopted to ensure that the physical boundary condition can be accurately satisfied. The present method is able to achieve a higher numerical accuracy than traditional IBM, which use the Delta function for interpolation. Some numerical validation tests are used for the validation of proposed method. The order and accuracy of the MLS approximation are tested by using a classical example of flow past a cylinder. Test of flow past the NACA0012 airfoil at different Mach numbers, angles of attack and Reynolds numbers is applied to verified the accuracy.

An explicit boundary condition-enforced immersed boundary-reconstructed thermal lattice Boltzmann flux solver for thermal–fluid–structure interaction problems with heat flux boundary conditions

For the thermal–fluid–structure interaction (TFSI) problems with moving boundaries, the original implicit boundary condition-enforced immersed boundary method (IBM) by Wang et al. [1] has to generate a large correlation matrix and compute its inversion at each iteration, implying that the virtual memory requirement and computational cost would grow exponentially with the number of Lagrangian points. In this work, we proposed an efficient explicit boundary condition-enforced immersed boundary method for Neumann boundary condition (NBC) to achieve high computational efficiency and maintain similar accuracy as the original implicit IBM [1], which circumvents the needs to assemble a large correlation matrix and inverse it in the original implicit IBM [1] through second-order approximation based on the error analysis using Taylor series expansion. Most importantly, the proposed explicit IBM can efficiently solve practical physics problems with a tremendous amount of Lagrangian points involving Neumann boundary condition. The comparisons of the virtual memory and computational cost between the explicit and implicit IBMs demonstrate that the explicit boundary condition-enforced IBM is not only computational efficient, but also has memory saving performance. The proposed explicit IBM integrated with the reconstructed thermal lattice Boltzmann flux solver (RTLBFS) is validated with some classical benchmarks, and the results show that the proposed explicit IBM can successfully resolve TFSI problems with Neumann boundary condition.

A high-order generalized differential quadrature method with lattice Boltzmann flux solver for simulating incompressible flows

This paper presents a high-order generalized differential quadrature method with lattice Boltzmann flux solver (LBFS-GDQ) for simulating incompressible isothermal flows. In this method, high-order polynomials are adopted to approximate both the solution and fluxes globally across the computational domain. Solution derivatives and flux divergence are conveniently computed by the GDQ method. At the interior solution points, the viscous and inviscid fluxes are evaluated simultaneously via LBFS. Treatments to prevent the global accuracy from being contaminated by the streaming error of LBFS are proposed and studied, including the choice for the local streaming spacing and interpolation methods for the local reconstruction. The present method inherits the advantages of both GDQ and LBFS, i.e., global spectral accuracy, direct evolution of macroscopic variables, and convenient implementation of boundary conditions. Numerical experiments with a wide selection of incompressible flow problems confirm the excellent accuracy, efficiency, and flexibility of the proposed method.

Modeling immiscible fluid flow in fractal pore medium by multiphase lattice Boltzmann flux solver

In this paper, the multiphase lattice Boltzmann flux solver (MLBFS), where the phase field model and the apparent liquid permeability model are built-in, is developed to simulate incompressible multiphase flows in fractal pore structure at the representative elementary volume scale. MLBFS takes advantage of the traditional Navier–Stokes solver (e.g., geometric flexibility and direct handling of complex boundary conditions) and lattice Boltzmann method (e.g., intrinsically kinetic nature, simplicity, and parallelism). It is easily applied to simulate multiphase flows transport in the porous medium with large density ratios and high Reynolds numbers. This study focuses on the fluid flow in fractal pore structures and provides an in-depth discussion of the effects of non-Newtonian index, fractal parameters, and density ratios on multiphase flow. The proposed model is validated with benchmark problems to test the applicability and reliability of the MLBFS in describing fluid flow in fractal pore structures with large density ratios and viscosity ratios. Simulation results show that the fractal parameters (i.e., fractal dimension, tortuous fractal dimension, porosity, and capillary radius ratio) can accurately characterize fractal pore structure and significantly affect the apparent liquid permeability. In addition, the flow rate increases with the fractal dimension and decreases with the tortuous fractal dimension, while both flow rate and apparent liquid permeability decrease as the capillary radius ratio. It is also noteworthy that the effect of nonlinear drag forces cannot be neglected for shear-thickened flows.