Navier–Stokes and Lattice–Boltzmann on octree‐like grids in the Peano framework

Mehl, Miriam; Neckel, Tobias; Neumann, Philipp

doi:10.1002/fld.2469

Cited by 18 publications

(15 citation statements)

References 50 publications

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“…Moreover, as the mesh grids are nonuniform, the total number of mesh grids can be reduced, which finally save the simulation time. Compared with other nonuniform mesh grid LB scheme, it is worth noticing that the MLUPS rate of the best results of our scheme is 1.6 times higher than that of the BGK LB on octree-like grids presented in [57] (performed on a 64-bit i7 quad core machine with 2.80 GHz and an 8-MB / 256-kB L3/L2 cache).…”

Section: Performancementioning

confidence: 81%

A lattice Boltzmann method for viscous free surface waves in two dimensions

Zhao

Huang

et al. 2012

Numerical Methods in Fluids

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SUMMARY We propose a new method based on the combination of the lattice Boltzmann equation (LBE) and the kinematic boundary condition (KBC) method to simulate viscous free surface wave in two dimensions. In our method, the flow field is modeled by LBE, whereas the free surface is explicitly tracked by the local height function, which is calculated by the KBC method. The free surface boundary condition (FSBC) for LBE is revised from previous researches. Interpolation‐supplemented lattice Boltzmann (ISLB) method is introduced, which enables our approach to be applied on arbitrary, nonuniform mesh grids. Five cases are simulated respectively to validate the LBE–KBC method: the stationary flow and the solitary waves simulated by the revised‐FSBC are more accurate than the one obtained by the former‐FSBC; numerical results of standing waves show that our method is compatible to the existing two‐dimensional finite‐volume scheme; cases of small amplitude Stokes wave and waves traveling over a submerged bar show good agreement on wave celerity, wavelength, wave amplitude and wave period between numerical results and corresponding analytical solutions and/or experiment data.Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Performancementioning

confidence: 81%

A lattice Boltzmann method for viscous free surface waves in two dimensions

Zhao

Huang

et al. 2012

Numerical Methods in Fluids

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“…We also show that our implementation can reach throughput rates of more than 1,000 time steps per second in a strong scaling scenario, enabling simulations that perform several million time steps per hour compute time. To the best knowledge of the authors, the total number of cells that can be handled as well as the overall performance achieved significantly exceed the data published for the LBM on non-uniform grids to date [21,30,40,51]. In addition to the algorithms and data structures, we also propose a method for scaling the two relaxation parameters of the two-relaxation-time collision model across different grid resolutions.…”

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confidence: 99%

Massively Parallel Algorithms for the Lattice Boltzmann Method on NonUniform Grids

Schornbaum¹,

Rüde²

2016

SIAM J. Sci. Comput.

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The lattice Boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large-scale non-stationary flow simulations, reaching up to a trillion (10 12 ) grid nodes. Additionally, grid refinement can lead to substantial savings in memory and compute time. These saving, however, come at the cost of much more complex data structures and algorithms. In particular, the interface between subdomains with different grid sizes must receive special treatment. In this article, we present parallel algorithms, distributed data structures, and communication routines that are implemented in the software framework waLBerla in order to support large-scale, massively parallel lattice Boltzmannbased simulations on non-uniform grids. Additionally, we evaluate the performance of our approach on two current petascale supercomputers. On an IBM Blue Gene/Q system, the largest weak scaling benchmarks with refined grids are executed with almost two million threads, demonstrating not only near-perfect scalability but also an absolute performance of close to a trillion lattice Boltzmann cell updates per second. On an Intel-based system, the strong scaling of a simulation with refined grids and a total of more than 8.5 million cells is demonstrated to reach a performance of less than one millisecond per time step. This enables simulations with complex, non-uniform grids and four million time steps per hour compute time.

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“…The Lattice Boltzmann model and the respective slip and transition flow extensions are implemented within the Lattice Boltzmann application [11,32] of the Peano framework [33]. This framework provides adaptive Cartesian grid structures that are traversed along the iterates of the space-filling Peano curve.…”

Section: The Peano Frameworkmentioning

confidence: 99%

Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

Neumann

Rohrmann²

2012

OJFD

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We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two-and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to further reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.

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Navier–Stokes and Lattice–Boltzmann on octree‐like grids in the Peano framework

Cited by 18 publications

References 50 publications

A lattice Boltzmann method for viscous free surface waves in two dimensions

A lattice Boltzmann method for viscous free surface waves in two dimensions

Massively Parallel Algorithms for the Lattice Boltzmann Method on NonUniform Grids

Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

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