Resolution sensitivity of momentum‐exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method

In the lattice Boltzmann method (LBM), the mechanism of fluid–solid interaction can be effectively captured by appropriately enforcing the no‐slip conditions in shear direction, and bounce‐back of the non‐equilibrium distribution portion in the normal direction at fluid–solid interfaces. Among various solid–fluid interaction schemes being proposed for LBM in recent decades, two simple fluid–solid interaction methods—the momentum exchange algorithm (MEA) and the immersed boundary scheme (IBS)—were developed based on the above concept. In this paper, MEA and IBS are implemented in a D2Q9 LBGK system and applied to measure the wall correction factors of drag force upon a stationary circular particle midway in the Poiseuille channel flow at very low Reynolds number and drag coefficients at low to moderate Reynolds numbers. MEA and IBS are also employed to compare the fluid‐induced torque over the cylinder in the Taylor–Couette flow, and the steady velocity of a particle settling under the influence of gravity inside a tube. The above experiments show that IBS seems to be more accurate and less demanding on lattice resolution. Copyright © 2010 John Wiley & Sons, Ltd.     

A hybrid immersed‐boundary and multi‐block lattice Boltzmann method for simulating fluid and moving‐boundaries interactions

A numerical method is developed for modelling the interactions between incompressible viscous fluid and moving boundaries. The principle of this method is introducing the immersed‐boundary concept in the framework of the lattice Boltzmann method, and improving the accuracy and efficiency of the simulation by refining the mesh near moving boundaries. Besides elastic boundary with a constitutive law, the method can also efficiently simulate solid moving‐boundary interacting with fluid by employing the direct forcing technique. The method is validated by the simulations of flow past a circular cylinder, two cylinders moving with respect to each other and flow around a hovering wing. The versatility of the method is demonstrated by the numerical studies including elastic filament flapping in the wake of a cylinder and fish‐like bodies swimming in quiescent fluid. Copyright © 2006 John Wiley & Sons, Ltd.     

An improved immersed boundary‐lattice Boltzmann method based on force correction technique

In this paper, an improved immersed boundary‐lattice Boltzmann method based on the force correction technique is presented for fluid‐structure interaction problems including the moving boundary interfaces. By introducing a force correction coefficient, the non‐slip boundary conditions are much better enforced compared with the conventional immersed boundary‐lattice Boltzmann methods. In addition, the implicit and iterative calculations are avoided; thus, the computational cost is reduced dramatically. Several numerical experiments are carried out to test the efficiency of the method. It is found that the method has the second‐order accuracy, and the non‐slip boundary conditions are enforced indeed. The numerical results also show that the present method is a suitable tool for fluid‐structure interaction problems involving complex moving boundaries.     

Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force

A method for direct numerical analysis of three‐dimensional deformable particles suspended in fluid is presented. The flow is computed on a fixed regular ‘lattice’ using the lattice Boltzmann method (LBM), where each solid particle is mapped onto a Lagrangian frame moving continuously through the domain. Instead of the bounce‐back method, an external boundary force (EBF) is used to impose the no‐slip boundary condition at the fluid–solid interface for stationary or moving boundaries. The EBF is added directly to the lattice Boltzmann equation. The motion and orientation of the particles are obtained from Newtonian dynamics equations. The advantage of this approach is outlined in comparison with the standard and higher‐order interpolated bounce‐back methods as well as the LBM immersed‐boundary and the volume‐of‐fluid methods. Although the EBF method is general, in this application, it is used in conjunction with the lattice–spring model for deformable particles. The methodology is validated by comparing with experimental and theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

On the immersed boundary‐lattice Boltzmann simulations of incompressible flows with freely moving objects

For simulating freely moving problems, conventional immersed boundary‐lattice Boltzmann methods encounter two major difficulties of an extremely large flow domain and the incompressible limit. To remove these two difficulties, this work proposes an immersed boundary‐lattice Boltzmann flux solver (IB‐LBFS) in the arbitrary Lagragian–Eulerian (ALE) coordinates and establishes a dynamic similarity theory. In the ALE‐based IB‐LBFS, the flow filed is obtained by using the LBFS on a moving Cartesian mesh, and the no‐slip boundary condition is implemented by using the boundary condition‐enforced immersed boundary method. The velocity of the Cartesian mesh is set the same as the translational velocity of the freely moving object so that there is no relative motion between the plate center and the mesh. This enables the ALE‐based IB‐LBFS to study flows with a freely moving object in a large open flow domain. By normalizing the governing equations for the flow domain and the motion of rigid body, six non‐dimensional parameters are derived and maintained to be the same in both physical systems and the lattice Boltzmann framework. This similarity algorithm enables the lattice Boltzmann equation‐based solver to study a general freely moving problem within the incompressible limit. The proposed solver and dynamic similarity theory have been successfully validated by simulating the flow around an in‐line oscillating cylinder, single particle sedimentation, and flows with a freely falling plate. The obtained results agree well with both numerical and experimental data. Copyright © 2016 John Wiley & Sons, Ltd.     

Unstructured lattice Boltzmann method in three dimensions

Over the last decade, the lattice Boltzmann method (LBM) has evolved into a valuable alternative to continuum computational fluid dynamics (CFD) methods for the numerical simulation of several complex fluid‐dynamic problems. Recent advances in lattice Boltzmann research have considerably extended the capability of LBM to handle complex geometries. Among these, a particularly remarkable option is represented by cell‐vertex finite‐volume formulations which permit LBM to operate on fully unstructured grids. The two‐dimensional implementation of unstructured LBM, based on the use of triangular elements, has shown capability of tolerating significant grid distortions without suffering any appreciable numerical viscosity effects, to second‐order in the mesh size. In this work, we present the first three‐dimensional generalization of the unstructured lattice Boltzmann technique (ULBE as unstructured lattice Boltzmann equation), in which geometrical flexibility is achieved by coarse‐graining the lattice Boltzmann equation in differential form, using tetrahedrical grids. This 3D extension is demonstrated for the case of 3D pipe flow and moderate Reynolds numbers flow past a sphere. The results provide evidence that the ULBE has significant potential for the accurate calculation of flows in complex 3D geometries. Copyright © 2005 John Wiley & Sons, Ltd.     

A spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for conjugate heat transfer applications

We present a spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for fluid–solid conjugate heat transfer applications. Using the discrete Boltzmann equation, we propose a numerical scheme for conjugate heat transfer applications on unstructured, non‐uniform grids. We employ a double‐distribution thermal lattice Boltzmann model to resolve flows with variable Prandtl (Pr) number. Based upon its finite element heritage, the spectral‐element discontinuous Galerkin discretization provides an effective means to model and investigate thermal transport in applications with complex geometries. Our solutions are represented by the tensor product basis of the one‐dimensional Legendre–Lagrange interpolation polynomials. A high‐order discretization is employed on body‐conforming hexahedral elements with Gauss–Lobatto–Legendre quadrature nodes. Thermal and hydrodynamic bounce‐back boundary conditions are imposed via the numerical flux formulation that arises because of the discontinuous Galerkin approach. As a result, our scheme does not require tedious extrapolation at the boundaries, which may cause loss of mass conservation. We compare solutions of the proposed scheme with an analytical solution for a solid–solid conjugate heat transfer problem in a 2D annulus and illustrate the capture of temperature continuities across interfaces for conductivity ratio γ > 1. We also investigate the effect of Reynolds (Re) and Grashof (Gr) number on the conjugate heat transfer between a heat‐generating solid and a surrounding fluid. Steady‐state results are presented for Re = 5?40 and Gr = 10⁵?10⁶. In each case, we discuss the effect of Re and Gr on the heat flux (i.e. Nusselt number Nu) at the fluid–solid interface. Our results are validated against previous studies that employ finite‐difference and continuous spectral‐element methods to solve the Navier–Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.     

A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast

A hybrid phase field multiple relaxation time lattice Boltzmann method (LBM) is presented in this paper for simulation of multiphase flows with large density contrast. In the present method, the flow field is solved by a lattice Boltzmann equation. Concurrently, the interface of two fluids is captured by solving the macroscopic Cahn‐Hilliard equation using the upwind scheme. To be specific, for simulation of the flow field, an lattice Boltzmann equation (LBE) model developed in Shao et al. (Physical Review E, 89 (2014), 033309) for consideration of density contrast in the momentum equation is used. Moreover, in the present work, the multiple relaxation time collision operator is applied to this LBE to enable simulation of problems with large viscosity contrast or high Reynolds number. For the interface capturing, instead of solving another set of LBE as in many phase field LBMs, the macroscopic Cahn‐Hilliard equation is directly solved by using a weighted essentially non‐oscillatory scheme. In this way, the present hybrid phase field LBM shares full advantages of the phase field LBM while enhancing numerical stability. The ability of the present method to simulate multiphase flow problems with large density contrast is demonstrated by several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

A coupled immersed boundary‐lattice Boltzmann method with smoothed point interpolation method for fluid‐structure interaction problems

The immersed boundary‐lattice Boltzmann method has been verified to be an effective tool for fluid‐structure interaction simulation associated with thin and flexible bodies. The newly developed smoothed point interpolation method (S‐PIM) can handle the largely deformable solids owing to its softened model stiffness and insensitivity to mesh distortion. In this work, a novel coupled method has been proposed by combining the immersed boundary‐lattice Boltzmann method with the S‐PIM for fluid‐structure interaction problems with large‐displacement solids. The proposed method preserves the simplicity of the lattice Boltzmann method for fluid solvers, utilizes the S‐PIM to establish the realistic constitutive laws for nonlinear solids, and avoids mesh regeneration based on the frame of the immersed boundary method. Both two‐ and three‐dimensional numerical examples have been carried out to validate the accuracy, convergence, and stability of the proposed method in consideration of comparative results with referenced solutions.     

Multi‐scale time integration for transient conjugate heat transfer

The quasi‐steady assumption is commonly adopted in existing transient fluid–solid‐coupled convection–conduction (conjugate) heat transfer simulations, which may cause non‐negligible errors in certain cases of practical interest. In the present work, we adopt a new multi‐scale framework for the fluid domain formulated in a triple‐timing form. The slow‐varying temporal gradient corresponding to the time scales in the solid domain has been effectively included in the fluid equations as a source term, whilst short‐scale unsteadiness of the fluid domain is captured by a local time integration at a given ‘frozen’ large scale time instant. For concept proof, validation and demonstration purposes, the proposed methodology has been implemented in a loosely coupled procedure in conjunction with a hybrid interfacing treatment for coupling efficiency and accuracy. The present results indicate that a much enhanced applicability can be achieved with relatively small modifications of existing transient conjugate heat transfer methods at little extra cost. Copyright © 2016 John Wiley & Sons, Ltd.     

Hybrid lattice Boltzmann finite‐difference simulation of axisymmetric swirling and rotating flows

The axisymmetric flows with swirl or rotation were solved by a hybrid scheme with lattice Boltzmann method for the axial and radial velocities and finite‐difference method for the azimuthal (or swirl) velocity and the temperature. An incompressible axisymmetric lattice Boltzmann D2Q9 model was proposed to solve the axial and radial velocities through inserting source terms into the two‐dimensional lattice Boltzmann equation. Present hybrid scheme was firstly validated by simulations of Taylor–Couette flows between two concentric cylinders. Then the benchmark problems of melt flow in Czochralski crystal growth were studied and accurate results were obtained. Numerical experiment demonstrated that present axisymmetric D2Q9 model is more stable than the previous axisymmetric D2Q9 model (J. Comp. Phys. 2003; 186 (1):295–307). Hence, compared with the previous model, present numerical method provides a significant advantage in simulation melt flow cases with high Reynolds number and high Grashof number. Copyright © 2006 John Wiley & Sons, Ltd.     

The simulation of turbulent particle‐laden channel flow by the Lattice Boltzmann method

We perform direct numerical simulation of three‐dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle‐laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high‐speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall‐normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls. Copyright © 2015 John Wiley & Sons, Ltd.     

A method for direct simulation of flexible fiber suspensions using lattice Boltzmann equation with external boundary force

The computational method presented here can be used to study the effect of volume fraction and particle deformation on the rheology and microstructure of deformable fibers suspended in Newtonian fluid. In this method, the flow is computed on a fixed regular ‘lattice’ using the lattice Boltzmann method, where each solid particle is mapped onto a Lagrangian frame moving continuously through the domain. Instead of the standard bounce-back method, an external boundary force is used to impose the no-slip boundary condition at the fluid–solid interface for stationary or moving boundaries. The motion and orientation of the fiber are obtained from Newtonian dynamics equations. Although the external boundary force method is general, in this application it is used in conjunction with a flexible fiber model, which calculates the flexible fiber deformation by the real material properties. The methodology is validated by comparing with experimental and theoretical results.     

On improvements of simplified and highly stable lattice Boltzmann method: Formulations,boundary treatment,and stability analysis

In this paper, we present a detailed report on a revised form of simplified and highly stable lattice Boltzmann method (SHSLBM) and its boundary treatment as well as stability analysis. The SHSLBM is a recently developed scheme within lattice Boltzmann framework, which utilizes lattice properties and relationships given by Chapman‐Enskog expansion analysis to reconstruct solutions of macroscopic governing equations recovered from lattice Boltzmann equation and resolved in a predictor‐corrector scheme. Formulations of original SHSLBM are slightly adjusted in the present work to facilitate implementation on body‐fitted mesh. The boundary treatment proposed in this paper offers an analytical approach to interpret no‐slip boundary condition, and the stability analysis in this paper fixes flaws in previous works and reveals a very nice stability characteristic in high Reynolds number scenarios. Several benchmark tests are conducted for comprehensive evaluation of the boundary treatment and numerical validation of stability analysis. It turns out that by adopting the modifications suggested in this work, lower numerical error can be expected.     

Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method

A hybrid Cartesian/immersed boundary code is developed and applied to interactions between a flexible plate and a surrounding fluid. The velocities at the immersed boundary (IB) nodes are reconstructed by interpolations along local normal lines to an interface. A new criterion is suggested to distribute the IB nodes near an interface. The suggested criterion guarantees a closed fluid domain by a set of the IB nodes and it is applicable to a zero‐thickness body. To eliminate the pressure interpolation at the IB nodes, the hybrid staggered/non‐staggered grid method is adapted. The developed code is validated by comparisons with other experimental and computational results of flow around an in‐line oscillating cylinder. Good agreements are achieved for velocity profiles and vorticity and pressure contours. As applications to the fluid–structure interaction, oscillations of flexible plate in a resting fluid and flow over a flexible plate are simulated. The elastic deformations of the flexible plate are modelled based on the equations of motion for plates considering the fluid pressure as the external load on the plate. Two non‐dimensional parameters are identified and their effects on the damping of the plate motion are examined. Grid convergence tests are carried out for both cases. Copyright © 2007 John Wiley & Sons, Ltd.     

Lattice‐Boltzmann and finite element simulations of fluid flow in a SMRX Static Mixer Reactor

A detailed comparison between the finite element method (FEM) and the lattice‐Boltzmann method (LBM) is presented. As a realistic test case, three‐dimensional fluid flow simulations in an SMRX static mixer were performed. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used as a highly efficient chemical reactor for viscous systems like polymers. The complex geometry of this mixer makes such three‐dimensional simulations non‐trivial. An excellent agreement between the results of the two simulation methods was found. Furthermore, the numerical results for the pressure drop as a function of the flow rate were close to experimental measurements. Results show that the relatively simple LBM is a good alternative to traditional methods. Copyright © 1999 John Wiley & Sons, Ltd.     

Lattice Boltzmann simulations for flow and heat/mass transfer problems in a three‐dimensional porous structure

The lattice Boltzmann method (LBM) for a binary miscible fluid mixture is applied to problems of transport phenomena in a three‐dimensional porous structure. Boundary conditions for the particle distribution function of a diffusing component are described in detail. Flow characteristics and concentration profiles of diffusing species at a pore scale in the structure are obtained at various Reynolds numbers. At high Reynolds numbers, the concentration profiles are highly affected by the flow convection and become completely different from those at low Reynolds numbers. The Sherwood numbers are calculated and compared in good agreement with available experimental data. The results indicate that the present method is useful for the investigation of transport phenomena in porous structures. Copyright © 2003 John Wiley & Sons, Ltd.     

A ghost fluid Lattice Boltzmann method for complex geometries

A ghost fluid Lattice Boltzmann method (GF‐LBM) is developed in this study to represent complex boundaries in Lattice Boltzmann simulations of fluid flows. Velocity and density values at the ghost points are extrapolated from the fluid interior and domain boundary via obtaining image points along the boundary normal inside the fluid domain. A general bilinear interpolation algorithm is used to obtain values at image points which are then extrapolated to ghost nodes thus satisfying hydrodynamic boundary conditions. The method ensures no‐penetration and no‐slip conditions at the boundaries. Equilibrium distribution functions at the ghost points are computed using the extrapolated values of the hydrodynamic variables, while non‐equilibrium distribution functions are extrapolated from the interior nodes. The method developed is general, and is capable of prescribing Dirichlet as well as Neumann boundary conditions for pressure and velocity. Consistency and second‐order accuracy of the method are established by running three test problems including cylindrical Couette flow, flow between eccentric rotating cylinders and flow over a cylinder in a confined channel. Copyright © 2011 John Wiley & Sons, Ltd.     

AN EVALUATION OF THE BOUNCE-BACK BOUNDARY CONDITION FOR LATTICE BOLTZMANN SIMULATIONS

The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltemann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0·1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder. The bounce-back boundary condition is shown to yield accurate lattice Boltzmann simulations with reduced computational requirements for computational grids of 170×170 or finer, a relaxation time less than 1·5 and any Reynolds number from 0·1 to 100. For this range of parameters the root mean square error in velocity and the relative error in drag coefficient are less than 1 per cent for the octagonal cylinder and 2 per cent for the circular cylinder. © 1997 John Wiley & Sons, Ltd.     

Application of the lattice‐Boltzmann method to study flow and dispersion in channels with and without expansion and contraction geometry

The lattice‐Boltzmann (LB) method, derived from lattice gas automata, is a relatively new technique for studying transport problems. The LB method is investigated for its accuracy to study fluid dynamics and dispersion problems. Two problems of relevance to flow and dispersion in porous media are addressed: (i) Poiseuille flow between parallel plates (which is analogous to flow in pore throats in two‐dimensional porous networks), and (ii) flow through an expansion–contraction geometry (which is analogous to flow in pore bodies in two‐dimensional porous networks). The results obtained from the LB simulations are compared with analytical solutions when available, and with solutions obtained from a finite element code (FIDAP) when analytical results are not available. Excellent agreement is found between the LB results and the analytical/FIDAP solutions in most cases, indicating the utility of the lattice‐Boltzmann method for solving fluid dynamics and dispersion problems. Copyright © 1999 John Wiley & Sons, Ltd.