Lattice Boltzmann Simulations with Locally Refined Meshes

Eitel-Amor, Georg; Meinke, Matthias; Schröder, Wolfgang

doi:10.2514/6.2011-3398

Cited by 4 publications

(3 citation statements)

References 40 publications

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“…To further examine the accuracy of the CFDLBM developed for 3‐D simulations, the present solution for the flow over the sphere with Re = 100 is compared with that of Eitel‐Amor et al obtained by the LBM with the local mesh refinement, as given in Table . As observed in this Table, they have used a number of cells of 1.5 × 10 6 for the discretization of a (64 D × 30 D × 30 D ) cube domain around the sphere.…”

Section: Numerical Resultsmentioning

confidence: 99%

Simulation of three‐dimensional incompressible flows in generalized curvilinear coordinates using a high‐order compact finite‐difference lattice Boltzmann method

Ezzatneshan

Hejranfar

2018

Numerical Methods in Fluids

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Summary In the present study, a high‐order compact finite‐difference lattice Boltzmann method is applied for accurately computing 3‐D incompressible flows in the generalized curvilinear coordinates to handle practical and realistic geometries with curved boundaries and nonuniform grids. The incompressible form of the 3‐D nineteen discrete velocity lattice Boltzmann method is transformed into the generalized curvilinear coordinates. Herein, a fourth‐order compact finite‐difference scheme and a fourth‐order Runge‐Kutta scheme are used for the discretization of the spatial derivatives and the temporal term, respectively, in the resulting 3‐D nineteen discrete velocity lattice Boltzmann equation to provide an accurate 3‐D incompressible flow solver. A high‐order spectral‐type low‐pass compact filtering technique is applied to have a stable solution. All boundary conditions are implemented based on the solution of the governing equations in the 3‐D generalized curvilinear coordinates. Numerical solutions of different 3‐D benchmark and practical incompressible flow problems are performed to demonstrate the accuracy and performance of the solution methodology presented. Herein, the 2‐D cylindrical Couette flow, the decay of a 3‐D double shear wave, the cubic lid‐driven cavity flow with nonuniform grids, the flow through a square duct with 90° bend and the flow past a sphere at different flow conditions are considered for validating the present computations. Numerical results obtained show the accuracy and robustness of the present solution methodology based on the implementation of the high‐order compact finite‐difference lattice Boltzman method in the generalized curvilinear coordinates for solving 3‐D incompressible flows over practical and realistic geometries.

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Section: Numerical Resultsmentioning

confidence: 99%

Simulation of three‐dimensional incompressible flows in generalized curvilinear coordinates using a high‐order compact finite‐difference lattice Boltzmann method

Ezzatneshan

Hejranfar

2018

Numerical Methods in Fluids

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“…Previous studies [12,15,20,21,34,35] have indicated that a quadratic or cubic interpolation is necessary to maintain the second order convergence of the LBM algorithm. However, Eitel et al [7,16] have obtained good results by using linear interpolations in combination with a subgrid-scale model. In the current study, the velocity is interpolated quadraticly by using a compact stencil and the velocity gradient information (i.e.…”

Section: Local Mesh Refinementmentioning

confidence: 99%

“…The equilibrium part on the other hand is directly interpolated between mesh resolutions. This idea has been adopted and further investigated in several studies since then [7,[10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Implementation of the compact interpolation within the octree based Lattice Boltzmann solver Musubi

Klimach

Roller

2019

Computers & Mathematics with Applications

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A sparse octree based parallel implementation of the lattice Boltzmann method for non-uniform meshes is presented in this paper. To couple grids of different resolutions, a second order accurate compact interpolation is employed and further extended into three dimensions. This compact interpolation requires only four source elements from the adjacent level for both two-and three dimensions.Thus, it reduces the computational and communication overhead in parallel executions. Moreover, the implementation of a weight based domain decomposition algorithm and level-wise elements arrangement are explained in details.The second order convergence of both velocity and strain rate are validated numerically in the Taylor-Green vortex test case. Additionally, the laminar flow around a cylinder at Re = 20, 100 and around a sphere at Re = 100 is investigated. Good agreement between simulated results and those from literature is observed, which provides further evidence for the accuracy of our method.

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Principles of Solution of the Governing Equations

Blažek¹

2015

Computational Fluid Dynamics: Principles and Applications

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Lattice Boltzmann Simulations with Locally Refined Meshes

Cited by 4 publications

References 40 publications

Simulation of three‐dimensional incompressible flows in generalized curvilinear coordinates using a high‐order compact finite‐difference lattice Boltzmann method

Simulation of three‐dimensional incompressible flows in generalized curvilinear coordinates using a high‐order compact finite‐difference lattice Boltzmann method

Implementation of the compact interpolation within the octree based Lattice Boltzmann solver Musubi

Principles of Solution of the Governing Equations

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