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SUMMARYIn order to find applicable treatments of moving boundary conditions based on the lattice Boltzmann method in flow acoustic problems, three bounce‐back (BB) methods and four kinds of immersed boundary (IB) methods are compared. We focused on fluid–solid boundary conditions for flow acoustic problems especially the simulations of sound waves from moving boundaries. BB methods include link bounce‐back, interpolation bounce‐back and unified interpolation bounce‐back methods. Five IB methods are explicit and implicit direct‐forcing (Explicit‐IB and Implicit‐IB), two kinds of partially saturated computational methods and ghost fluid method. In order to reduce the spurious pressure generated by the fresh grid node changing from solid domain to fluid domain for BB methods and sharp IB methods, we proposed two new kinds of treatments and compared them with two existing ones. Simulations of the benchmark problems prove that the local evolutionary iteration (LI) is the best one in treatments of the fresh nodes. In addition, for standing boundary problems, although BB methods have a little higher accuracy, all the methods have similar accuracy. However, for moving boundary problems, IB methods are more appropriate than BB methods, because IB methods' smooth interpolation of pressure eld produces less disturbing spurious pressure waves. With improved treatments of fresh nodes, BB methods are also acceptable for moving boundary acoustic problems. In comparative tests in respective type, unified interpolation bounce‐back with LI, Implicit‐IB, and ghost fluid with LI are the best choices. Copyright © 2013 John Wiley & Sons, Ltd.

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The recently developed multiphase lattice Boltzmann flux solver (MLBFS) overcomes the limitations in the multiphase lattice Boltzmann method (MLBM), such as the coupled time step and mesh step, uniform meshes, and complex distribution functions (DFs) treatment at the boundary. Unlike the original MLBFS deduced from the standard lattice Boltzmann method, an improved multiphase lattice Boltzmann flux solver (IMLBFS) is proposed based on the Chapman–Enskog analysis of the MLBM which has a source term stemming from the density contrast and surface tension force. In this way, the surface tension force is considered when reconstructing the numerical interface fluxes, which gives the present method stronger physical basis. As a result, the IMLBFS is more stable than the MLBFS. Moreover, the IMLBFS simplifies the process of reconstructing interface fluxes and avoids the complicated calculation of the source term in the MLBM. Some moments of the DFs and source terms are directly given as macroscopic variables to avoid additional computations and storage. This strategy ensures that the IMLBFS even has higher computational efficiency than the MLBFS. To test the proposed IMBFS for large-density-ratio flows, complex interfacial changes and high Reynolds number (up to 10 000), several typical problems are studied, including the static Laplace law, the droplet spreading on a flat surface, the unsteady Rayleigh–Taylor instability, the bubble rising under buoyancy, and the droplet splashing on a thin film. Simulations suggest that the present method predicts smaller spurious velocities, and it is more stable and efficient than the original MLBFS.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Four slip boundary conditions are presented for liquid flow. • The proposed schemes surmount the barrier of limited slip length. • The proposed schemes are specified by the slip length. • Two slip boundary conditions are suitable for curved walls.