A Simplified Lattice Boltzmann Method without Evolution of Distribution Function

Жен, Чен; Chen, Shu; Wang, Yan; Yang, Liuming; Tan, Danielle

doi:10.4208/aamm.oa-2016-0029

Cited by 74 publications

(52 citation statements)

References 45 publications

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“…To overcome these drawbacks, a simplified LBM (SLBM) was recently developed . In the SLBM, the macroscopic equations recovered by lattice Boltzmann equation (LBE) are resolved by a predictor‐corrector scheme, which are then reconstructed by the lattice properties and the relationships given by Chapman‐Enskog expansion analysis; and the final formulations only involve the equilibrium and the nonequilibrium distribution functions.…”

Section: Introductionmentioning

confidence: 99%

On improvements of simplified and highly stable lattice Boltzmann method: Formulations, boundary treatment, and stability analysis

Жен

Chen

Tan

et al. 2018

Numerical Methods in Fluids

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Summary In this paper, we present a detailed report on a revised form of simplified and highly stable lattice Boltzmann method (SHSLBM) and its boundary treatment as well as stability analysis. The SHSLBM is a recently developed scheme within lattice Boltzmann framework, which utilizes lattice properties and relationships given by Chapman‐Enskog expansion analysis to reconstruct solutions of macroscopic governing equations recovered from lattice Boltzmann equation and resolved in a predictor‐corrector scheme. Formulations of original SHSLBM are slightly adjusted in the present work to facilitate implementation on body‐fitted mesh. The boundary treatment proposed in this paper offers an analytical approach to interpret no‐slip boundary condition, and the stability analysis in this paper fixes flaws in previous works and reveals a very nice stability characteristic in high Reynolds number scenarios. Several benchmark tests are conducted for comprehensive evaluation of the boundary treatment and numerical validation of stability analysis. It turns out that by adopting the modifications suggested in this work, lower numerical error can be expected.

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Section: Introductionmentioning

confidence: 99%

On improvements of simplified and highly stable lattice Boltzmann method: Formulations, boundary treatment, and stability analysis

Жен

Chen

Tan

et al. 2018

Numerical Methods in Fluids

Self Cite

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“…Recognizing that

f_{α}^{\sim}

is continuous over the physical space, the linear extrapolation scheme is adopted here to determine its boundary value. This strategy has been adopted in the simulation of Newtonian fluid flows . Given the fact that this quantity is a minor term in the order of O ( δ t ), the linear extrapolation scheme would not deteriorate the global second‐order accuracy.…”

Section: Simplified Lattice Boltzmann Methods For Non‐newtonian Power‐mentioning

confidence: 99%

“…The simplified LBM (SLBM) is a recent exploration towards eliminating or alleviating limitations of the conventional LBM . Instead of directly evolving the distribution functions, SLBM reconstructs solutions to the macroscopic equations recovered from LBE through the Chapman‐Enskog (C‐E) expansion analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The simplified LBM (SLBM) is a recent exploration towards eliminating or alleviating limitations of the conventional LBM. 29,30 Instead of directly evolving the distribution functions, SLBM reconstructs solutions to the macroscopic equations recovered from LBE through the Chapman-Enskog (C-E) expansion analysis. The second-order accuracy is preserved in the reconstruction process, and the final formulations reflect direct evolution of the macroscopic variables.…”

Section: Introductionmentioning

confidence: 99%

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Simplified lattice Boltzmann method for non‐Newtonian power‐law fluid flows

Жен

Chen

2019

Numerical Methods in Fluids

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Summary In this paper, we present a simplified lattice Boltzmann method for non‐Newtonian power‐law fluid flows. The new method adopts the predictor‐corrector scheme and reconstructs solutions to the macroscopic equations recovered from the lattice Boltzmann equation through Chapman‐Enskog expansion analysis. The truncated power‐law model is incorporated into this method to locally adjust the physical viscosity and the associated relaxation parameter, which recovers the non‐Newtonian behaviors. Compared with existing non‐Newtonian lattice Boltzmann models, the proposed method directly evolves the macroscopic variables instead of the distribution functions, which eliminates the intrinsic drawbacks like high cost in virtual memory and inconvenient implementation of physical boundary conditions. The validity of the method is demonstrated by benchmark tests and comparisons with analytical solution or numerical results in the literature. Benchmark solutions to the three‐dimensional lid‐driven cavity flow of non‐Newtonian power‐law fluid are also provided for future reference.

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“…To overcome or alleviate these drawbacks, a simplified lattice Boltzmann method (SLBM) was recently developed and extended to simulations of thermal flows [11,12]. Simplified thermal lattice Boltzmann method (STLBM) is derived from reconstructing solutions to the macroscopic governing equations recovered from lattice Boltzmann equation and resolved in a predictor-corrector scheme.…”

Section: Introductionmentioning

confidence: 99%

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

2017

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An unconditionally stable thermal lattice Boltzmann method (USTLBM) is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE) through Chapman-Enskog (C-E) expansion analysis are resolved in a predictor-corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM). Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.

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A Simplified Lattice Boltzmann Method without Evolution of Distribution Function

Cited by 74 publications

References 45 publications

On improvements of simplified and highly stable lattice Boltzmann method: Formulations, boundary treatment, and stability analysis

On improvements of simplified and highly stable lattice Boltzmann method: Formulations, boundary treatment, and stability analysis

Simplified lattice Boltzmann method for non‐Newtonian power‐law fluid flows

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

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