Simulation of three‐dimensional flows over moving objects by an improved immersed boundary–lattice Boltzmann method

An improved immersed boundary–lattice Boltzmann method (IB–LBM) developed recently [28] was applied in this work to simulate three‐dimensional (3D) flows over moving objects. By enforcing the non‐slip boundary condition, the method could avoid any flow penetration to the wall. In the developed IB–LBM solver, the flow field is obtained on the non‐uniform mesh by the efficient LBM that is based on the second‐order one‐dimensional interpolation. As a consequence, its coefficients could be computed simply. By simulating flows over a stationary sphere and torus [28] accurately and efficiently, the proposed IB–LBM showed its ability to handle 3D flow problems with curved boundaries. In this paper, we further applied this method to simulate 3D flows around moving boundaries. As a first example, the flow over a rotating sphere was simulated. The obtained results agreed very well with the previous data in the literature. Then, simulation of flow over a rotating torus was conducted. The capability of the improved IB–LBM for solving 3D flows over moving objects with complex geometries was demonstrated via the simulations of fish swimming and dragonfly flight. The numerical results displayed quantitative and qualitative agreement with the date in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Towards simulation of flapping wings using immersed boundary method

In this work the immersed boundary method is applied to simulate incompressible turbulent flows around stationary and moving objects. The goal is to demonstrate that the immersed boundary technique along with a large eddy simulation approach is capable of simulating the effect of the so‐called leading edge vortex (LEV), which can be found in flapping wing aerodynamics. A Lagrangian method is used to approximate the solutions in the freshly cleared cells that lay within solid objects at one time step and emerge into fluid domain at the next time step. Flow around a stationary cylinder at Re_D = 20, 40, and 3900 (based on cylinder diameter D) is first studied to validate the immersed boundary solver based on the finite volume scheme using a staggered grid. Then, a harmonically oscillating cylinder at Re_D = 10 000 is considered to test the solver after the Lagrangian method is implemented to interpolate the solution in the freshly cleared cells. Finally, this approach is used to study flows around a stationary flat‐plate at several angles of attack and fast pitching flat‐plate. The rapidly pitching plate creates a dynamic LEV that can be used to improve the efficiency of flapping wings of micro air vehicle and to determine the optimum flapping frequency. Copyright © 2012 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.     

A direct‐forcing pressure‐based lattice Boltzmann method for solving fluid–particle interaction problems

A direct‐forcing immersed boundary‐lattice Boltzmann method (IB–LBM) is developed to simulate fluid–particle interaction problems. This method uses the pressure‐based LBM to solve the incompressible flow field and the immersed boundary method to handle the fluid–particle interactions. The pressure‐based LBM uses the pressure distribution functions instead of the density distribution functions as the independent dynamic variables. The main idea is to explicitly eliminate the compressible effect due to the density fluctuation. In the IB method, a direct‐forcing method is introduced to capture the particle motion. It directly computes an IB force density at each lattice grid from the differences between the pressure distribution functions obtained by the LBM and the equilibrium pressure distribution functions computed from the particle velocity. By applying this direct‐forcing method, the IB–LBM becomes a purely LBM version. Also, by applying the Gauss theorem, the formulas for computing the force and the torque acting on the particle from the flows are derived from the volume integrals over the particle volume instead of from the surface integrals over the particle surface. The order of accuracy of the IB–LBM is demonstrated on the errors of velocity field, wall stress, and gradients of velocity and pressure. As a demonstration of the efficiency and capabilities of the new method, sedimentation of a large number of spherical particles in an enclosure is simulated. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical and numerical studies of the boundary slip in the immersed boundary‐thermal lattice Boltzmann method

We analytically and numerically investigate the boundary slip, including the velocity slip and the temperature jump, in immersed boundary‐thermal lattice Boltzmann methods (IB‐TLBMs) with the two‐relaxation‐time collision operator. We derive the theoretical equation for the relaxation parameters considering the effect of the advection velocity on the temperature jump of the IB‐TLBMs. The analytical and numerical solutions demonstrate that the proposed iterative correction methods without the computational cost of the sparse matrix solver reduce the boundary slip and boundary‐value deviation as effectively as the implicit correction method for any relaxation time. Because the commonly used multi‐direct forcing method does not consider the contributions of the body force to the momentum flux, it cannot completely eliminate the boundary slip because of the numerical instability for a long relaxation time. Both types of proposed iterative correction methods are more numerically stable than the implicit correction method. In simulations of flow past a circular cylinder and of natural convection, the present iterative correction methods yield adequate results without the errors of the velocity slip, the temperature jump, and the boundary‐value deviation for any relaxation time parameters and for any number of Lagrangian points per length. The combination of the present methods and the two‐relaxation‐time collision operator is suitable for simulating fluid flow with thermal convection in the multiblock method in which the relaxation time increases in inverse proportion to the grid size.     

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.     

基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

采用浸没边界格子Boltzmann(immersed boundary-lattice Boltzmann,IB-LB)模型执行动边界绕流数值模拟时,信息交互界面和边界力计算格式直接影响流动求解器的数值精度和计算效率.基于隐式扩散界面,一种改进的直接力格式IB-LB模型被提出.边界力表达式基于欧拉/拉格朗日变量同一性准...     

An SPH model for free surface flows with moving rigid objects

This paper presents a computational model for free surface flows interacting with moving rigid bodies. The model is based on the SPH method, which is a popular meshfree, Lagrangian particle method and can naturally treat large flow deformation and moving features without any interface/surface capture or tracking algorithm. Fluid particles are used to model the free surface flows which are governed by Navier–Stokes equations, and solid particles are used to model the dynamic movement (translation and rotation) of moving rigid objects. The interaction of the neighboring fluid and solid particles renders the fluid–solid interaction and the non‐slip solid boundary conditions. The SPH method is improved with corrections on the SPH kernel and kernel gradients, enhancement of solid boundary condition, and implementation of Reynolds‐averaged Navier–Stokes turbulence model. Three numerical examples including the water exit of a cylinder, the sinking of a submerged cylinder and the complicated motion of an elliptical cylinder near free surface are provided. The obtained numerical results show good agreement with results from other sources and clearly demonstrate the effectiveness of the presented meshfree particle model in modeling free surface flows with moving objects. Copyright © 2013 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.     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Moving least squares reconstruction for sharp interface immersed boundary methods

We propose a new approach for reconstructing velocity boundary conditions in sharp-inerface immersed boundary (IB) methods based on the moving least squares (MLS) interpolation method. The MLS is employed to not only reconstruct velocity boundary conditions but also to calculate the pressure and velocity gradients in the vicinity of the immersed body, which are required in fluid structure interaction problems to obtain the force exerted by the fluid on the structure. To extend the method to arbitrarily complex geometries with nonconvex shaped boundaries, the visibility method is combined with the MLS method. The performance of the proposed curvilinear IB MLS (CURVIB-MLS) is demonstrated by systematic grid-refinement studies for two- and three-dimensional tests and compared with the standard CURVIB method employing standard wall-normal interpolation for reconstructing boundary conditions. The test problems are flow in a lid-driven cavity with a sphere, uniform flow over a sphere, flow on a NACA0018 airfoil at incidence, and vortex-induced vibration of an elastically-mounted cylinder. We show that the CURVIB-MLS formulation yields a method that is easier to implement in complex geometries and exhibits higher accuracy and rate of convergence relative to the standard CURVIB method. The MLS approach is also shown to dramatically improve the accuracy of calculating the pressure and viscous forces imparted by the flow on the body and improve the overall accuracy of FSI simulations. Finally, the CURVIB-MLS approach is able to qualitatively capture on relatively coarse grids important features of complex separated flows that the standard CURVIB method is able to capture only on finer grids.     

An immersed boundary method for the incompressible Navier–Stokes equations in complex geometry

A nodally exact convection–diffusion–reaction scheme developed in Cartesian grids is applied to solve the flow equations in irregular domains within the framework of immersed boundary (IB) method. The artificial momentum forcing term applied at certain points in the flow and inside the body of any shape allows the imposition of no‐slip velocity condition to account for the body of complex boundary. Development of an interpolation scheme that can accurately lead to no‐slip velocity condition along the IB is essential since Cartesian grid lines generally do not coincide with the IB. The results simulated from the proposed IB method agree well with other numerical and experimental results for several chosen benchmark problems. The accuracy and fidelity of the IB flow solver to predict flows with irregular IBs are therefore demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.     

不可压缩机翼绕流的有限谱法计算

结合有限谱QUICK格式求解不可压缩粘性流问题。这一格式用于模拟不同攻角下的NACA1200机翼绕流问题。利用体积力,提出了将流场速度从0加速到来流速度的方法。区别于传统的压力梯度为零的边界条件,推导出一个更精确的压力边界条件。为使速度散度保持为零,在泊松方程中给速度散度一个特殊的处理。这一成果说明了有限谱法不但具有很高的精度,而且能灵活地和其他格式一起构造出新的格式,从而成功地应用到复杂流场不可压缩流动的数值计算中。     

过渡区气体微尺度流动的格子Boltzmann模拟

采用格子Boltzmann方法(LBM)对过渡区内的微尺度气体流动进行了模拟研究. 在已有滑移区微流动LBM模型中引入Knudsen层速度修正,选取合适的修正函数表达式并依据动理论确定了可调参数的合理取值. 在边界条件的处理格式上,采用了适合过渡区模拟的高阶滑移边界的替代格式来捕捉过渡区微流动的滑移速度,避免了直接求解高阶速度导数项的数值困难. 通过对两类不同的微流动进行模拟的结果表明:与数值解吻合得较好,尤其是对Kn>0.5微流动滑移速度的预测,与已有LBM的模拟结果相比有明显的提高.      

An improved near‐wall modeling for large‐eddy simulation using immersed boundary methods

An improved near‐wall modeling for large‐eddy simulation using the immersed boundary method is proposed. It is shown in this study that the existing near‐wall modeling for the immersed boundary (IB) methods that imposes the velocity boundary condition at the IB node is not sufficient to enforce a correct wall shear stress at the IB node. A new method that imposes a shear stress condition through the modification of the subgrid scale‐eddy viscosity at the IB node is proposed. In this method, the subgrid eddy viscosity at the IB node is modified such that the viscous flux at the face adjacent to the IB node correctly approximates the total shear stress. The method is applied to simulate the fully developed turbulent flows in a plane channel and a circular pipe. It is demonstrated that the new method improves the prediction of the mean velocity and turbulence stresses in comparison with the existing wall modeling based solely on the velocity boundary condition. Copyright © 2015 John Wiley & Sons, Ltd.     

A local domain‐free discretization method for simulation of incompressible flows over moving bodies

This paper presents a local domain‐free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier–Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of ‘freshly cleared nodes/cells’ encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite‐element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual‐time‐stepping scheme based on artificial compressibility. In order to validate the present method for moving‐boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in‐line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving–pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. Copyright © 2010 John Wiley & Sons, Ltd.     

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

In this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k ? ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k ? ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.     

Efficient coupling of direct forcing immersed boundary-lattice Boltzmann method and finite element method to simulate fluid-structure interactions

Fluid-structure interactions (FSI) of rigid and flexible bodies are simulated in this article. For the fluid flow, multidirect forcing immersed boundary method (IBM) is adopted to capture the moving boundary, and lattice Boltzmann method (LBM) is used to evolve the flow field. Compared with our previous no-penetration IBM, less iterations are required in this work. In addition, larger velocity in lattice units can be used and the nonphysical force oscillations are suppressed due to the C³ 6-point kernel. Multi-relaxation-time collision operator and local grid refinement are also adopted in LBM to enhance the numerical stability and efficiency. To improve the efficiency of the FSI coupling algorithm, the mesh of the deformable structure can be coarser than the Lagrangian mesh using Newton-Cotes formulas to integrate the traction on the structure surface. A variety of benchmarks, including flow around a circular cylinder with Reynold number ranging from 20 to 200, forced oscillation of a circular cylinder, vortex-induced vibration (VIV) of an elastically mounted circular cylinder in two degrees of freedom, and VIV of an elastic cantilever beam attached to a circular cylinder, are carried out to evaluate the accuracy and stability of the present coupling algorithm. For the benchmark FSI problem considered in this article, a reduction of 54% of the calculation time is achieved using coarser structure mesh. As an application of the FSI coupling algorithm, the mechanism of an elastic beam in the wake of a circular cylinder is discussed.     

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.     

An immersed boundary finite difference method for LES of flow around bluff shapes

A three‐dimensional numerical model using large eddy simulation (LES) technique and incorporating the immersed boundary (IMB) concept has been developed to compute flow around bluff shapes. A fractional step finite differences method with rectilinear non‐uniform collocated grid is employed to solve the governing equations. Bluff shapes are treated in the IMB method by introducing artificial force terms into the momentum equations. Second‐order accurate interpolation schemes for all sorts of grid points adjacent to the immersed boundary have been developed to determine the velocities and pressure at these points. To enforce continuity, the methods of imposition of pressure boundary condition and addition of mass source/sink terms are tested. It has been found that imposing suitable pressure boundary condition (zero normal gradient) can effectively reproduce the correct pressure distribution and enforce mass conservation around a bluff shape. The present model has been verified and applied to simulate flow around bluff shapes: (1) a square cylinder and (2) the Tsing Ma suspension bridge deck section model. Complex flow phenomena such as flow separation and vortex shedding are reproduced and the drag coefficient, lift coefficient, and pressure coefficient are calculated and analyzed. Good agreement between the numerical results and the experimental data are obtained. The model is proven to be an efficient tool for flow simulation around bluff bodies in time varying flows. Copyright © 2004 John Wiley & Sons, Ltd.