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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.

A sharp-interface immersed boundary lattice Boltzmann method (IBLBM) is developed to reduce spurious-pressure oscillations in moving boundary problems. We adopt a cut-cell-based method, i.e., the partially saturated computational cell method, because the primary cause of spurious-pressure oscillations is the failure to obey the geometric conservation law near the boundary in the sharp-interface IBLBM. We modify a sharp-interface IBLBM (ghost fluid method) to fit the cut-cell approach. This boundary condition can guarantee the Dirichlet and Neumann boundary conditions for velocity and pressure. Some simulations are shown to test the validity of the method, including a circular cylinder with motions that are at rest, moving, oscillatory, and neutrally buoyant. The results illustrate that the method reduces effectively spurious pressure and can simulate moving boundary problems, especially when pressure field accuracy is a key concern.

Based on the Navier slip model, a slip boundary format for the lattice Boltzmann method is developed for curve walls of which the shape is well considered. The main idea of this method is to convert the slip length into the slip velocity with a simplified algorithm. With the Navier slip model, the slip velocities at the boundary are obtained through the interpolation of the fluid points near the boundary and are then substituted into the velocity boundary conditions to construct the relationship between the slip length and the macroscopic flow field. This format is free from the restriction of the previous combined boundary conditions which can only be applied to flat boundaries. It also overcomes the limitation that the slip boundary can only simulate flows with small slip length. The present slip boundary condition is implemented for the lattice Bhatnagar-Gross-Krook model, which is verified by several cases, including the cylindrical Couette flow and the irregular Poiseuille flow. The numerical results agree well with theoretical analysis. Furthermore, this boundary condition is applied to the hydrofoil to study the drag reduction effect of the boundary slip phenomenon. It is found that the slip boundary can effectively reduce the drag of the hydrofoil at low Reynolds numbers. Moreover, the position of the slip boundary on the hydrofoil also has significant effects on the lift-to-drag ratio.

Most conventional axisymmetric multiphase lattice Boltzmann methods involve complicated external source terms to model the axisymmetric effect. Besides, the break of mass conservation for each phase and the limitation of the simulated density ratio are still critical issues. To remove these drawbacks, a mass-conserved fractional step axisymmetric multiphase lattice Boltzmann flux solver is developed for flows with a large density ratio. We aim to naturally combine the developed modified Cahn–Hilliard equation with a small mass correction term, the lattice Boltzmann flux solver, and the fractional step method together for the simulation of the axisymmetric multiphase flows. The governing equations in the axisymmetric framework are split into the predictor and corrector steps. The predictor step without considering the axisymmetric effect and the mass correction term is solved by the finite-volume multiphase lattice Boltzmann flux solver based on the local application of the lattice Boltzmann method. Then, the corrector step is performed to include the axisymmetric effect and the mass correction term. Specifically, the numerical implementation of the mass correction term is designed in the axisymmetric framework. Several axisymmetric multiphase cases, including the Laplace law, the droplet oscillation, merging spherical bubbles, and micro-droplet impacting on a dry hydrophobic plate, have been adopted to demonstrate the accuracy and reliability of the proposed method. The results of the Laplace law and the droplet oscillation show that for one time step, solving the modified Cahn–Hilliard equation by our method can save about 46% of the computational time as compared with the fifth-order upwind scheme.