Finite Element Based Formulation of the Lattice Boltzmann Equation

Jo, Jong Chull; Roh, Kyung Wan; Kwon, Young W.

doi:10.5516/net.2009.41.5.649

Cited by 5 publications

(6 citation statements)

References 8 publications

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“…In order to compare the LBM and the FVM solutions, we need to use the non-dimensional end-time T = 21 5 for the LBM solver. As we cannot find grid sizes for which the time step dt is a divisor of the dimensionless end-time T = 21 5 , we need to take into account Figure 5: L 2 -error in the macroscopic variables for a monotaomic gas on the spatial domain X = [0; 2) 3 at time t = 2 for the D3Q7 velocity set and initial conditions (23). that we are comparing slightly different end-times for the FVM-and LBMsolutions.…”

Section: Dmentioning

confidence: 99%

“…In the next section, we will use this Maxwellian as equilibrium distribution in the derivation of a linearized semi-discrete version of equation ( 5) for monoatomic gases. Throughout this paper, we will refer to these semi-discrete models as Finite Discrete Velocity Models (FDVM) though in literature also the names discrete Boltzmann equation [33], differential form of the Lattice Boltzmann Equation [41], and Lattice Boltzmann Equation [23] are used. We will only refer to the linearized fully-discrete version of equation ( 5) derived in section 6 as Lattice Boltzmann Equation (LBE).…”

Section: By Comparison Of the Moments Regardingmentioning

confidence: 99%

“…L 2 -error in the macroscopic variables for a diatomic gas on the domain X = [0, 2] 3 at time t = 2 for the D3Q7 velocity set and initial conditions(23).…”

mentioning

confidence: 99%

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Derivation and analysis of Lattice Boltzmann schemes for the linearized Euler equations

Otte

Frank

2016

Computers & Mathematics with Applications

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We derive Lattice Boltzmann (LBM) schemes to solve the Linearized Euler Equations in 1D, 2D, and 3D with the future goal of coupling them to an LBM scheme for Navier Stokes Equations and an Finite Volume scheme for Linearized Euler Equations. The derivation uses the analytical Maxwellian in a BGK model. In this way, we are able to obtain second-order schemes. In addition, we perform an L 2 -stability analysis. Numerical results validate the approach.

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Section: Dmentioning

confidence: 99%

Section: By Comparison Of the Moments Regardingmentioning

confidence: 99%

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Derivation and analysis of Lattice Boltzmann schemes for the linearized Euler equations

Otte

Frank

2016

Computers & Mathematics with Applications

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“…They investigated the effect of the terms which coupled the fluid flow with the fluid mesh motion on the convergence behavior of the overall solution procedure and also indicated that the computational efficiency of the simulation of many FSI processes, including fluid flow through flexible pipes, could be increased significantly if some coupling terms were calculated exactly. Jo et al 6 developed the finite element based on lattice Boltzmann method to model complex fluid domain shapes. Their study addressed a new finite element formulation of the lattice Boltzmann equation using a general weighted residual technique.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation and transonic wind-tunnel test for elastic thin-shell structure considering fluid–structure interaction

Yan

Zhu-you

Zhang

2015

Chinese Journal of Aeronautics

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Aerodynamic force can lead to the strong structural vibration of flying aircraft at a high speed. This harmful vibration can bring damage or failure to the electronic equipment fixed in aircraft. It is necessary to predict the structural dynamic response in the design course. This paper presents a new numerical algorithm and scheme to solve the structural dynamics responses when considering fluid-structure interaction (FSI). Numerical simulation for a free-flying structural model in transonic speed is completed. Results show that the small elastic deformation of the structure can greatly affect the FSI. The FSI vibration tests are carried out in a transonic speed windtunnel for checking numerical theory and algorithms, and the wind-tunnel test results well accord with that of the numerical simulation. This indicates that the presented numerical method can be applied to predicting the structural dynamics responses when containing the FSI. ª 2015 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

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“…Furthermore, they require recalculations of the collision for each refinement level. To avoid this, a second approach is used, which uncouples the time and space increments and uses conventional computational fluid dynamic (CFD) methods such as the finitevolume method (FVM) [17][18][19][20][21][22], the finite-difference method (FDM) [23][24][25][26][27][28][29][30][31][32][33][34], the finiteelement method (FEM) [35][36][37][38][39][40][41], or the meshless method [42][43][44][45]. This approach suffers from numerical diffusion, which leads to dissipation error in proportion to the mesh distribution.…”

Section: Introductionmentioning

confidence: 99%

Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

2022

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The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function is perfectly shifted to the neighbor node on the uniform mesh arrangement. This advantage may curtail the applicability of the method to problems with complex geometries. To overcome this issue, a high-order meshless interpolation-based approach is proposed to handle the streaming step. Owing to its high accuracy, the radial basis function (RBF) is one of the popular methods used for interpolation. In general, RBF-based approaches suffer from some stability issues, where their stability strongly depends on the shape parameter of the RBF. In the current work, a stabilized RBF approach is used to handle the streaming. The stabilized RBF approach has a weak dependency on the shape parameter, which improves the stability of the method and reduces the dependency of the shape parameter. Both the stabilized RBF method and the streaming of the LBM are used for solving three benchmark problems. The results of the stabilized method and the perfect streaming LBM are compared with analytical solutions or published results. Excellent agreements are observed, with a little advantage for the stabilized approach. Additionally, the computational cost is compared, where a marginal difference is observed in the favor of the streaming of the LBM. In conclusion, one could report that the stabilized method is a viable alternative to the streaming of the LBM in handling both simple and complex geometries.

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Finite Element Based Formulation of the Lattice Boltzmann Equation

Cited by 5 publications

References 8 publications

Derivation and analysis of Lattice Boltzmann schemes for the linearized Euler equations

Derivation and analysis of Lattice Boltzmann schemes for the linearized Euler equations

Numerical simulation and transonic wind-tunnel test for elastic thin-shell structure considering fluid–structure interaction

Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

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