Lattice Boltzmann Solution Research Articles

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

Stratified Taylor–Green vortex by lattice Boltzmann methods: Influence of stencils, forcing schemes, and collision models

Stably stratified Taylor–Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier–Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.

Lattice Boltzmann method with nonreflective boundary conditions for low Mach number combustion

The paper presents a lattice Boltzmann (LB) method for premixed and nonpremixed combustion simulations with nonreflective boundary conditions, in contrast to Navier–Stokes solvers or hybrid schemes. The current approach employs different sets of distribution functions for flow, temperature and species fields, which are fully coupled. The discrete equilibrium density distributions are obtained from the Hermite expansions thus thermal compressibility is included. The coupling among the momentum, energy and species transport enables the model to be applicable for reactive flows with chemical heat release. The characteristic boundary conditions are incorporated into the LB scheme to avoid numerical reflections. The multi-relaxation-time collision schemes are applied to all the LB solution procedures to improve numerical stability. With detailed thermodynamics and chemical mechanisms for hydrogen-air, the LB modelling framework is validated against both premixed flame propagation and nonpremixed counterflow diffusion flame benchmarks. Simulations of circular expanding premixed flames further demonstrate the capability of the new reactive LB method. The developed LB methodology retains the advantages of classic LB methods and extends the LB capability to low Mach number combustion with potential applications in mesoscale and microscale combustors, catalysis, fuel cells, batteries and so on.

An implicit high-order radial basis function-based differential quadrature-finite volume method on unstructured grids to simulate incompressible flows with heat transfer

A high-order implicit radial basis function-based differential quadrature-finite volume (IRBFDQ-FV) method is presented in this work to efficiently simulate incompressible flows with heat transfer on unstructured mesh. The velocity and temperature fields are solved by locally using the lattice Boltzmann flux solver and the high-order finite volume method. Specifically, the proposed highly accurate finite volume method utilizes a high-order Taylor polynomial to approximate the solution within every control cell. Spatial derivatives are the corresponding coefficients in the polynomial, and they are approximated by the meshless radial basis function-based differential quadrature (RBFDQ) method. The diffusive and convective fluxes at each cell interface are simultaneously evaluated through local reconstruction of lattice Boltzmann solution using D2Q9 lattice velocity model. To efficiently calculate the solution with high-order accuracy, an implicit time-marching method incorporating the lower-upper symmetric Gauss-Seidel (LU-SGS) and the explicit first stage, singly-diagonally implicit Runge-Kutta (ESDIRK) approaches is devised. The proposed method is comprehensively validated by a series of numerical experiments containing both steady-state and time-dependent heat transfer problems with/without curved boundaries at a wide variety of Rayleigh numbers and Grashof numbers. The obtained results demonstrate a high degree of accuracy and reliability of the proposed method for complex flows on unstructured mesh. In comparison with the classical second-order method, the proposed high-order method has better computational efficiency when comparable results are achieved.

Improved thermal energy storage with metal foam enhanced phase change materials considering various pore arrangements: A pore-scale parallel lattice Boltzmann solution

Low thermal conductivity of the phase change materials (PCMs) is the main impediment that causes avoiding their extensive usage for thermal energy storage. Metal foams can be used with PCMs to overcome this weakness to reach an enhanced PCM. The main challenge of using metal foam is to reach the optimal geometrical, mechanical, and physical properties to meet the desired performance. This study investigates the effect of pore arrangement in a homogenous closed-cell aluminum metal foam. Afterward, a comparison is presented between various arrangements and pore diameters to examine the effect of pore configuration and diameter on thermal energy storage performance. Three pore arrangements are considered: Simple (simple linear arrangement of pores); Staggered (straticulate/alternative arrangement of pores); and Dots (simple pores with smaller ones diagonally placed between them). To simulate the melting process coupled with conduction and natural convection, the parallel lattice Boltzmann solver (PALABOS) –an open-source library consists of various predefined functions to solve complex thermo-fluidic problems– with enthalpy-based method is developed, and the results are validated. Different numerical simulations have been done to conduct the parameter study. In general, the Dots arrangement is relatively more effective than the two other studied arrangements. For dp = 5 mm, the melting times of PCM for all cases are similar to one another. However, for dp = 10 mm, the Dots arrangement could reduce the melting time by 20% compared to Staggered and Simple arrangements.

Hybrid lattice-Boltzmann digital-waveguide simulation of wind instruments

A hybrid lattice-Boltzmann digital-waveguide model is proposed to improve the efficiency of the computational aeroacoustics modeling of wind instruments. The nonlinear sound generator and the assumed linear resonator of a wind instrument are modeled separately using the lattice Boltzmann (LB) method and digital waveguide (DWG) method, correspondingly. Their coupling is achieved through the characteristic boundary condition, which breaks down the lattice Boltzmann solutions at the junction into separated traveling waves along different characteristic lines. The lattice Boltzmann solver then sends the outgoing acoustic wave to the digital waveguide, and receives the incoming acoustic wave to complete the boundary condition. Two examples are tested to demonstrate the validity of the proposed method, including a hybrid cylindrical pipe composed of two coupled cylindrical segments, one represented by LB and the other by DWG, and a hybrid single-reed instrument that comprises an LB mouthpiece-reed system and a DWG pipe.

Modified lattice Boltzmann solution for non-isothermal rarefied gas flow through microchannel utilizing BSR and second-order implicit schemes

Thermal microscale gas flow was simulated into a coplanar microchannel was simulated at a broad range of Knudsen numbers. Attempts were made to improve the accuracy of slip velocity on walls using a modified model with two relaxation times based upon the mesoscopic method. The temperature jump of fluid flow at the wall was captured by a model with a single relaxation time using a second-order implicit method. The Zou–He boundary conditions were employed at both inlet and outlet boundaries, and bounce-back/specular reflection distribution functions were applied to the impermeable walls. The non-equilibrium distribution functions were also used as the inlet temperature boundary condition. A fully developed temperature profile was considered at the microchannel outlet. A pressure ratio of 2 was considered in the simulations, and various parameters such as dimensionless pressure, pressure deviation from the linear pressure, dimensionless velocity at various Knudsen numbers, centerline velocity and slip velocity of the fluid, centerline temperature and fluid temperature on the wall, Nusselt number with changing Knudsen and Prandtl numbers, parameter k along the microchannel length and Cf·Re values were evaluated in the slip and transition flow regimes. The results of the direct simulation Monte Carlo were used to evaluate the correctness of the numerical model. The consistency of the two methods indicated the accuracy of the proposed method.

A preconditioned lattice Boltzmann flux solver for steady flows on unstructured hexahedral grids

The lattice Boltzmann flux solver (LBFS), first introduced by Shu et al. (2014) on structured meshes, allows fluid flow problems to be solved on unstructured meshes discretised by the finite volume method. The solver calculates the macroscopic fluxes at the cell interfaces from a local reconstruction of the lattice Boltzmann solution. In this paper the LBFS is extended to three-dimensional unstructured hexahedral meshes and a preconditioned lattice Boltzmann flux solver (PLBFS) is presented. The PLBFS involves applying the preconditioning technique proposed by Guo (2004) to the LBFS and is achieved by modifying the equilibrium distribution function used to calculate the macroscopic fluxes at the cell interface. When the PLBFS is applied to steady flow problems, it is shown that convergence is significantly accelerated and the accuracy of predictions with unstructured grids is greatly improved when compared to the LBFS. This paper also introduces a strategy for choosing the optimal value of preconditioning factor with unstructured hexahedral meshes.

Does MCWASP still follow Moore’s law? Forty years of advances in microstructure modeling

Over the past forty years, the series of MCWASP conferences has been the witness of the fantastic developments in the field of modeling of welding and solidification processes. This has been made possible thanks to the exponential increase in computing power but also to the emergence of new numerical methods and tools. While the “size” of computer simulations reported in MCWASP proceedings continues to follow Moore’s law describing the evolution of computers power, the present contribution focuses on the evolution of microstructure modeling. In this respect, a major turning point is the introduction of the phase field (PF) method in the mid-90’s. While PF is still the method of choice for the direct simulation of microstructure formation, it is also very CPU intensive. Therefore, it did not replace and rather complement other coarser methods such as analytical micro-macro models, Cellular Automata coupled with Finite Elements (so-called CAFE approach), modified-CAFE methods, mesoscopic model based on a dendrite envelope or Dendritic Needle Network (DNN) model. Some of these models as well as PF are coupled with fluid flow models based either on standard Navier-Stokes or Lattice-Boltzmann solutions. In parallel to these developments, wonderful experimental tools have become available to complement and validate numerical simulations: in situ X-ray radiography and tomography, EBSD, atom probe, FIB, etc. Besides a review of the past forty years, the present contribution will outline future directions of research in the area of microstructure modeling.

CFD analysis of a check valve from SAFRAN Helicopter Engines using a Lattice-Boltzmann solution

Unsteady Computational Fluid Dynamics (CFD) solvers with accurate turbulence modelling are increasingly required to solve real industrial problematics where most applications include complex moving parts, highly turbulent flows and transient phenomena. Most of these industrial requirements are out of reach for the traditional CFD solutions based on steady state or unsteady Reynolds-Averaged Navier-Stokes (RANS) turbulence approaches and with limited capabilities to deal with moving parts and Fluid-Structure Interaction (FSI). XFlow is the innovative CFD software developed by Next Limit Dynamics to deal with this increasing demand on new industrial applications. XFlow features a particle-based discretization approach that uses a state-of-the-art Lattice-Boltzmann Method (LBM) to discretize the continuous Boltzmann equation, a time evolution equation for statistical probability distribution functions that describe accurately the behavior of a fluid. This proprietary particle-based kinetic solver implements at collision operator a Large Eddy Simulation (LES) turbulence model fully coupled with a generalized law of the wall (WMLES) in order to solve the transient turbulent effects usually observed on industrial applications. The aim of the work presented in this paper is to demonstrate the capability of the XFlow approach to predict costly instability issues of the Check Valves (CV) integrated inside the fuel circuit in helicopter engines. The results of XFlow will be compared to the experimental measurements provided by SAFRAN Helicopter Engines on one of their CV designs during real working conditions. The CV dynamics will be modelled in XFlow as a rigid body with one degree of freedom along the axis aligned with the flow direction. A spring effort is modelled with a pre-load force and a stiffness. With these two parameters, XFlow computes dynamically the valve position according to the dynamic movement equation based on the hydraulic and spring forces applied on. As preliminary step, different fixed flow-rate boundary conditions will be applied at the inlet of the CV in order to validate the global valve characteristics with the incompressible solver. The CV oscillations are studied considering acoustics with an additional bulk viscosity term inside the flow equations. An increasing inlet volumetric flow law is applied to compute the dynamic response of the valve and to predict the frequency and the flow-rate range at which instabilities appear. This simulation shows a good agreement; the experimental instability range is well predicted as the eigen frequency.

High-order least-square-based finite-difference-finite-volume method for simulation of incompressible thermal flows on arbitrary grids.

In this work, a high-order (HO) least-square-based finite difference-finite volume (LSFD-FV) method together with thermal lattice Boltzmann flux solver (TLBFS) is presented for simulation of two-dimensional (2D) incompressible thermal flows on arbitrary grids. In the present method, a HO polynomial based on Taylor series expansion is applied within each control cell, where the unknown spatial derivatives at each cell center are approximated by least-square-based finite difference (LSFD) scheme. Then the recently developed TLBFS is applied to evaluate the convective and diffusive fluxes simultaneously at the cell interface by local reconstruction of thermal lattice Boltzmann solutions of the density and internal energy distribution functions. The present HO LSFD-FV method is verified and validated by 2D incompressible heat transfer problems. Numerical results indicate that the present method can be effectively and flexibly applied to solve thermal flow problems with curved boundaries on arbitrary grids. Compared with the conventional low-order finite volume method, higher efficiency and lower memory cost make the present HO method more promising for practical thermal flow problems.

Kinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods

A novel hybrid computational method based on the discrete-velocity (DV) approximation, including the lattice-Boltzmann (LB) technique, is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows, and LB schemes are employed in continuum flow zones. The schemes are written under the finite-volume (FV) formulation to achieve the flexibility of local mesh refinement. The truncated Hermite polynomial expansion is used for matching of DV and LB solutions. Special attention is paid to preserving conservation properties in the coupling algorithm. The test results obtained for the Couette flow of a rarefied gas are in excellent agreement with the benchmark solutions, mostly thanks to mesh refinement (both in the physical and velocity spaces) in the Knudsen layer.

A high order least square-based finite difference-finite volume method with lattice Boltzmann flux solver for simulation of incompressible flows on unstructured grids

This paper presents a high order least square-based finite difference-finite volume (LSFD-FV) method together with lattice Boltzmann flux solver for accurate simulation of incompressible flows on unstructured grids. Within each control cell, a high order polynomial, which is based on Taylor series expansion, is applied to approximate the solution function. The derivatives in the Taylor series expansion are approximated by the functional values at the centers of neighboring cells using the mesh-free least square-based finite difference (LSFD) method developed by Ding et al. (2004) [36]. In the high order finite volume method, the recently developed lattice Boltzmann flux solver (LBFS) is applied to evaluate the inviscid and viscous fluxes physically and simultaneously at the cell interface by local reconstruction of lattice Boltzmann solution. Compared with traditional k-exact high-order finite volume method, the present method is more accurate and efficient. Various benchmark examples are tested to validate the high-order accuracy, high computational efficiency and flexibility of the proposed method on unstructured grids.

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 solution of advection-dominated mass transport problem: a comparison

This article addresses the abilities and limitations of the Lattice Boltzmann (LB) method in solving advection-dominated mass transport problems. Several schemes of the LB method, including D2Q4, D2Q5, and D2Q9, were assessed in the simulation of two-dimensional advection-dispersion equations. The concept of Single Relaxation Time (SRT) and Multiple Relaxation Time (MRT) in addition to linear and quadratic Equilibrium Distribution Functions (EDF) were taken into account. The results of LB models were compared to the well-known Finite Difference (FD) solutions, including Explicit Finite Difference (EFD) and Crank-Nicolson (CN) methods. All LB models are more accurate than the aforementioned FD schemes. The results also indicate the high potency of D2Q5 SRT and D2Q9 SRT in describing advection-controlled mass transfer problems. The numerical artificial oscillations are observed when the Grid Peclet Number (GPN) is greater than 10, 25, 20, 25, and 10 regarding D2Q4 SRT, D2Q5 SRT, D2Q5 MRT, D2Q9 SRT and D2Q9 MRT, respectively, while the corresponding GPN values obtained for the EFD and CN methods were 2 and 5, respectively. Finally, a coupled system of groundwater and solute transport equations were solved satisfactorily using several LB models. Considering computational time, all LB models are much faster than CN method.

An effective lattice Boltzmann flux solver on arbitrarily unstructured meshes

The recently proposed lattice Boltzmann flux solver (LBFS) is a new approach for the simulation of incompressible flow problems. It applies the finite volume method (FVM) to discretize the governing equations, and the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. In the previous application of the LBFS, the structured meshes have been commonly employed, which may cause inconvenience for problems with complex geometries. In this paper, the LBFS is extended to arbitrarily unstructured meshes for effective simulation of incompressible flows. Two test cases, the lid-driven flow in a triangular cavity and flow around a circular cylinder, are carried out for validation. The obtained results are compared with the data available in the literature. Good agreement has been achieved, which demonstrates the effectiveness and reliability of the LBFS in simulating flows on arbitrarily unstructured meshes.

Numerical investigation of flow characteristics around two side-by-side cylinders by immersed boundary-lattice Boltzmann flux solver

In this paper, to study the characteristics of the flow in a laminar regime, an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) is applied to numerically simulate the unsteady viscous flows around two fixed and rotating circular cylinders in side-by-side arrangement. This method applies finite volume discretization to solve the macroscopic governing equations with the flow variables defined at cell centers. At the cell interface, numerical fluxes are physically evaluated by a local lattice Boltzmann solution. In addition, the no-slip boundary condition is accurately imposed by using the implicit boundary condition-enforced immersed boundary method. Due to the simplicity and high efficiency of IB-LBFS on non-uniform grids, it is suitable for simulating fluid flows with complex geometries and moving boundaries. Firstly, numerical simulations of laminar flow past two side-by-side cylinder are performed with different gap spacings at Reynolds numbers of 100 and 200. The simulation results show that a small gap spacing induces a biased flow and forms an irregular big wake behind two cylinders at a low Reynolds number. As the gap spacing increases, an in-phase or anti-phase flow is observed. Then, the effects of the main important parameters on flow characteristics are analyzed for flow past two side-by-side rotating cylinders, including the rotational speed, Reynolds number, and gap spacing. As the rotational speed is increased, the numerical results illustrate that unsteady wakes are suppressed and the flow becomes steady. As the gap spacing is increased, two separate vortex streets behind each cylinder are formed with a definite phase relationship and single shedding frequency.

Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

method combining the immersed boundary technique and a multi-relaxation-time (MRT) lattice Boltzmann flux solver (LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations (LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

Lattice Boltzmann solution of the transient Boltzmann transport equation in radiative and neutron transport.

Applications of the transient Boltzmann transport equation (BTE) have undergone much investigation, such as radiative heat transfer and neutron transport. This paper provides a lattice Boltzmann model to efficiently resolve the multidimensional transient BTE. For a higher angular resolution, enough transport directions are considered while the transient BTE in each direction is treated as a conservation law equation and solved independently. Both macroscopic equations recovered from a Chapman-Enskog expansion and simulated results of typical benchmark problems show not only the second-order accuracy but also the flexibility and applicability of the proposed lattice Boltzmann model. This approach may contribute a powerful technique for the parallel simulation of large-scale engineering and some alternative perspectives for solving the nonlinear transport problem further.

Maxwell iteration for the lattice Boltzmann method with diffusive scaling.

In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.