Comparison of free-surface and conservative Allen–Cahn phase-field lattice Boltzmann method

Schwarzmeier, Christoph; Holzer, Markus; Mitchell, Travis; Lehmann, Moritz F.; Häusl, Fabian; Rüde, Ulrich

doi:10.1016/j.jcp.2022.111753

Cited by 21 publications

(16 citation statements)

References 68 publications

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“…More noticeable differences are visible in the later course of the simulation. However, it must be pointed out that the FSLBM requires the wave's amplitude to range over at least one, but preferably multiple interface cells to capture the interface's motion significantly well 17 . This deficiency of the FSLBM is also visible in the grid convergence study provided in Figure B1 in Appendix B.0.1.…”

Section: Resultsmentioning

confidence: 99%

“…This section compares the boundary condition variants introduced and analyzed in Section 3 using five numerical experiments. The chosen test cases are partly identical to the ones suggested in prior articles 17,22 . They include the simulation of a standing gravity wave, the collapse of a rectangular and cylindrical liquid column, the rise of a Taylor bubble, and the impact of a drop into a thin film of liquid.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…They include the simulation of a standing gravity wave, the collapse of a rectangular and cylindrical liquid column, the rise of a Taylor bubble, and the impact of a drop into a thin film of liquid. The description of the test cases, simulation setups, and figures are similar to those from References 17,22 but are repeated here for completeness. All simulations were performed with double‐precision floating‐point arithmetic.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The domain's side walls in

x

‐ and y ‐direction were periodic, whereas the domain's top and bottom walls in z ‐direction were set to no‐slip. C. Schwarzmeier, M. Holzer, T. Mitchell, M. Lehmann, F. Häusl, U. Rüde, Comparison of free surface and conservative Allen–Cahn phase field lattice Boltzmann method, arXiv preprint, 17 2022; licensed under a Creative Commons Attribution (CC BY) license; the colors were changed from the original. [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Additionally, the FSLBM's algorithm is relatively complicated when compared to phase‐field models, for example. More details on the FSLBM's advantages and disadvantages, and a comparison with an Allen–Cahn LBM phase‐field model are presented in prior work 17 …”

Section: Introductionmentioning

confidence: 99%

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Analysis and comparison of boundary condition variants in the free‐surface lattice Boltzmann method

Schwarzmeier

Rüde

2023

Numerical Methods in Fluids

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The accuracy of the free‐surface lattice Boltzmann method (FSLBM) depends significantly on the boundary condition employed at the free interface. Ideally, the chosen boundary condition balances the forces exerted by the liquid and gas pressure. Different variants of the same boundary condition are possible, depending on the number and choice of the particle distribution functions (PDFs) to which it is applied. This study analyzes and compares four variants, in which (i) the boundary condition is applied to all PDFs oriented in the opposite direction of the free interface's normal vector, including or (ii) excluding the central PDF. While these variants overwrite existing information, the boundary condition can also be applied (iii) to only missing PDFs without dropping available data or (iv) to only missing PDFs but at least three PDFs as suggested in the literature. It is shown that neither variant generally balances the forces exerted by the liquid and gas pressure at the free surface. The four variants' accuracy was compared in five different numerical experiments covering various applications. These include a standing gravity wave, a rectangular and cylindrical dam break, a rising Taylor bubble, and a droplet impacting a thin pool of liquid. Overall, variant (iii) was substantially more accurate than the other variants in the numerical experiments performed in this study.

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Section: Resultsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

“…The domain's side walls in

x

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis and comparison of boundary condition variants in the free‐surface lattice Boltzmann method

Schwarzmeier

Rüde

2023

Numerical Methods in Fluids

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Multiphase lattice Boltzmann flux solver with conservative Allen‐Cahn model for modeling high‐density‐ratio flows

Chen,

Sun

2024

Numerical Methods in Fluids

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In this paper, the Allen‐Cahn‐Multiphase lattice Boltzmann flux solver (AC‐MLBFS) is proposed as a new and effective numerical simulation method for multiphase flows with high density ratios. The MLBFS resolves the macroscopic governing equations with the finite volume method and reconstructs numerical fluxes on the cell interface from local solutions to the lattice Boltzmann equation, which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann methods for simulating incompressible multiphase flows while alleviating their limitations. Previous MLBFS‐based multiphase solvers performed poorly in mass conservation, which might be caused by the excessive numerical diffusion in the Cahn‐Hilliard (CH) model used as the interface tracking algorithm. To resolve this problem, the present method proposes using the conservative Allen‐Cahn (AC) model as the interfacial tracking algorithm, which can ease the numerical implementation by removing high order derivative terms and alleviate mass leakage by enforcing local mass conservation in the physical model. Numerical validations will be carried out through benchmark tests at high density ratios and in extreme conditions with large Reynolds or Weber numbers. Through these examples, the accuracy and robustness as well as the mass conservation characteristics of the proposed method are demonstrated.

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Performance analysis of the free surface lattice Boltzmann implementation in waLBerla

Plewinski,

Alt,

Köstler

et al. 2024

Proc Appl Math and Mech

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The free‐surface lattice Boltzmann method uses a volume of fluid approach to simulate immiscible two‐fluid flow problems. It divides the simulation domain into three distinct phases—gas, fluid, and interface—where computation within the gas phase is disregarded. The interface delineates a one‐cell‐thick layer between the first two phases, validated physically for implementation in the HPC C++ multiphysics framework waLBerla but lacking an exhaustive performance analysis. This paper aims to shed light on node‐level performance on different architectures, employing continuous benchmarking, showing and analyzing weak scaling results on a modern HPC cluster, the Fritz supercomputer, and reporting energy consumption for the current implementation.

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Comparison of free-surface and conservative Allen–Cahn phase-field lattice Boltzmann method

Cited by 21 publications

References 68 publications

Analysis and comparison of boundary condition variants in the free‐surface lattice Boltzmann method

Analysis and comparison of boundary condition variants in the free‐surface lattice Boltzmann method

Multiphase lattice Boltzmann flux solver with conservative Allen‐Cahn model for modeling high‐density‐ratio flows

Performance analysis of the free surface lattice Boltzmann implementation in waLBerla

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