Immersed Boundary-Lattice Boltzmann Coupling Scheme for Fluid-Structure Interaction with Flexible Boundary

2011 ◽  
Vol 9 (5) ◽  
pp. 1375-1396 ◽  
Author(s):  
Yongguang Cheng ◽  
Hui Zhang ◽  
Chang Liu
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lattice Boltzmann ◽  
Immersed Boundary ◽  
Coupling Scheme ◽  
Structure Interaction ◽  
Large Pressure ◽  
Large Pressure Gradient ◽  
Complex Boundary ◽  
Ib Method

AbstractCoupling the immersed boundary (IB) method and the lattice Boltzmann (LB) method might be a promising approach to simulate fluid-structure interaction (FSI) problems with flexible structures and complex boundaries, because the former is a general simulation method for FSIs in biological systems, the latter is an efficient scheme for fluid flow simulations, and both of them work on regular Cartesian grids. In this paper an IB-LB coupling scheme is proposed and its feasibility is verified. The scheme is suitable for FSI problems concerning rapid flexible boundary motion and a large pressure gradient across the boundary. We first analyze the respective concepts, formulae and advantages of the IB and LB methods, and then explain the coupling strategy and detailed implementation procedures. To verify the effectiveness and accuracy, FSI problems arising from the relaxation of a distorted balloon immersed in a viscous fluid, an unsteady wake flow caused by an impulsively started circular cylinder at Reynolds number 9500, and an unsteady vortex shedding flow past a suddenly started rotating circular cylinder at Reynolds number 1000 are simulated. The first example is a benchmark case for flexible boundary FSI with a large pressure gradient across the boundary, the second is a fixed complex boundary problem, and the third is a typical moving boundary example. The results are in good agreement with the analytical and existing numerical data. It is shown that the proposed scheme is capable of modeling flexible boundary and complex boundary problems at a second-order spatial convergence; the volume leakage defect of the conventional IB method has been remedied by using a new method of introducing the unsteady and non-uniform external force; and the LB method makes the IB method simulation simpler and more efficient.

Numerical investigation of nonlinear fluid–structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

2018 ◽  
Vol 29 (04) ◽  
pp. 1850038 ◽  
Author(s):  
Chun-Lin Gong ◽  
Zhe Fang ◽  
Gang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lattice Boltzmann ◽  
Fluid Structure Interaction ◽  
Numerical Approach ◽  
Immersed Boundary ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Flexible Objects ◽  
Element Method

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid–structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

Simulation of Fluid–Structure Interaction Problems with Thin Elastic Plate via the Coupling of Finite Element and Lattice Boltzmann Methods

2020 ◽  
Vol 17 (10) ◽  
pp. 2050013
Author(s):  
Fei Jiang ◽  
Kangping Liao ◽  
Kazuki Matsumura ◽  
Junji Ohgi ◽  
Xian Chen
Keyword(s):  
Finite Element ◽  
Lattice Boltzmann ◽  
Fluid Structure Interaction ◽  
Immersed Boundary ◽  
Thin Elastic Plate ◽  
Computational Accuracy ◽  
Fe Method ◽  
Fluid Structure ◽  
Lattice Boltzmann Methods ◽  
Structure Interaction

A numerical framework is proposed to couple the finite element (FE) and lattice Boltzmann methods (LBM) for simulating fluid–structure interaction (FSI) problems. The LBM is used as an efficient method for solving the weakly-compressible fluid flows. The corotational FE method for beam elements is used to solve the thin plate deformation. The two methods are coupled via a direct-forcing immersed boundary (IB) method with a sub-iteration scheme. A virtual structure method has been developed to improve the computational accuracy. Validations of the proposed coupling method have been carried out by testing a vortex-induced vibration problem. The numerical results are in good agreement with [Li and Favier (2017), “A non-staggered coupling of finite element and lattice Boltzmann methods via an immersed boundary scheme for fluid-structure interaction,” Comput. Fluids 143, 90–102]. The proposed method does not require heavy linear algebra calculation, which is suitable for parallel computation.

A Lattice Boltzmann-Immersed Boundary-Finite Element Method for Nonlinear Fluid–Solid Interaction Simulation with Moving Objects

2018 ◽  
Vol 15 (07) ◽  
pp. 1850063 ◽  
Author(s):  
Chunlin Gong ◽  
Zhe Fang ◽  
Gang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lattice Boltzmann ◽  
Moving Objects ◽  
Moving Boundaries ◽  
Immersed Boundary ◽  
Nonlinear Fem ◽  
Ib Method ◽  
Nonlinear Fluid ◽  
Element Method

A nonlinear finite element method (FEM) was introduced into the immersed boundary (IB) — lattice Boltzmann method (LBM) framework to simulate the nonlinear fluid–solid interactions for moving deformable objects in incompressible fluid flow. The fluid motion is obtained by solving the discrete lattice Boltzmann equation, the moving boundaries of the solids are handled by the IB method, and the nonlinear dynamics of the deforming/moving objects are calculated by nonlinear FEM solvers in which the structural nodes are also set as Lagrangian markers to track the moving boundaries of the structures in IB method. The simulation results indicate that the proposed IB-LBM-FEM simulation framework not only satisfies the nonslip boundary condition well at the boundary points, but also has better accuracy for capturing nonlinearity because of its mature nonlinear FEM solver.

Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGK Model

2014 ◽  
Vol 16 (1) ◽  
pp. 136-168 ◽  
Author(s):  
Yongguang Cheng ◽  
Luoding Zhu ◽  
Chunze Zhang
Keyword(s):  
Lattice Boltzmann ◽  
Numerical Study ◽  
Rigid Wall ◽  
Segment Length ◽  
Immersed Boundary ◽  
Coupling Scheme ◽  
Circular Membrane ◽  
Shearing Flow ◽  
Dirac Delta ◽  
Forcing Term

AbstractThis paper aims to study the numerical features of a coupling scheme between the immersed boundary (IB) method and the lattice Boltzmann BGK (LBGK) model by four typical test problems: the relaxation of a circular membrane, the shearing flow induced by a moving fiber in the middle of a channel, the shearing flow near a non-slip rigid wall, and the circular Couette flow between two inversely rotating cylinders. The accuracy and robustness of the IB-LBGK coupling scheme, the performances of different discrete Dirac delta functions, the effect of iteration on the coupling scheme, the importance of the external forcing term treatment, the sensitivity of the coupling scheme to flow and boundary parameters, the velocity slip near non-slip rigid wall, and the origination of numerical instabilities are investigated in detail via the four test cases. It is found that the iteration in the coupling cycle can effectively improve stability, the introduction of a second-order forcing term in LBGK model is crucial, the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability, and the emergence of both temporal and spatial fluctuations of boundary parameters seems to be the indication of numerical instability. These elaborate results shed light on the nature of the coupling scheme and may benefit those who wish to use or improve the method.

Benchmark numerical solutions for two-dimensional fluid–structure interaction involving large displacements with the deforming-spatial-domain/stabilized space–time and immersed boundary–lattice Boltzmann methods

2017 ◽  
Vol 232 (14) ◽  
pp. 2500-2514 ◽  
Author(s):  
Yuan-Qing Xu ◽  
Yan-Qun Jiang ◽  
Jie Wu ◽  
Yi Sui ◽  
Fang-Bao Tian
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Fluid Structure Interaction ◽  
Spatial Domain ◽  
Space Time ◽  
Immersed Boundary ◽  
Flexible Plate ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Boltzmann Method

Body-fitted and Cartesian grid methods are two typical types of numerical approaches used for modelling fluid–structure interaction problems. Despite their extensive applications, there is a lack of comparing the performance of these two types of approaches. In order to do this, the present paper presents benchmark numerical solutions for two two-dimensional fluid–structure interaction problems: flow-induced vibration of a highly flexible plate in an axial flow and a pitching flexible plate. The solutions are obtained by using two partitioned fluid–structure interaction methods including the deforming-spatial-domain/stabilized space–time fluid–structure interaction solver and the immersed boundary–lattice Boltzmann method. The deforming-spatial-domain/stabilized space–time fluid–structure interaction solver employs the body-fitted-grid deforming-spatial-domain/stabilized space–time method for the fluid motions and the finite-difference method for the structure vibrations. A new mesh update strategy is developed to prevent severe mesh distortion in cases where the boundary does not oscillate periodically or needs a long time to establish a periodic motion. The immersed boundary–lattice Boltzmann method uses lattice Boltzmann method as fluid solver and the same finite-difference method as structure solver. In addition, immersed boundary method is used in the immersed boundary–lattice Boltzmann solver to handle the fluid–structure interaction coupling. Results for the characteristic force coefficients, tail position, plate deformation pattern and the vorticity fields are presented and discussed. The present results will be useful for evaluating the performance and accuracy of existing and new numerical methodologies for fluid–structure interaction.

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