Search

The recently developed lattice Boltzmann flux solver (PLBFS) for the incompressible porous flow is free from the limitations of coupled streaming time step and the mesh spacing, and the uniform meshes and the complex distribution function treatment at the boundary. However, the local flux reconstruction is inconsistent with the global governing equations in PLBFS. To overcome the drawback, a consistent generalized lattice Boltzmann flux solver for the incompressible porous flow is proposed based on the generalized lattice Boltzmann method (GLBM). The recovered macroscopic governing equations given by the Chapman–Enskog analysis of GLBM are globally resolved by the finite volume method. Specifically, the macroscopic variables are updated at cell centers using the three-step Runge–Kutta method, while the solution of the GLBM is locally applied for the fluxes reconstruction at cell interfaces. Unlike the PLBFS, the forcing term can be naturally incorporated into the interface fluxes reconstruction, which gives the present method a stronger physical basis and ensures global consistency. Moreover, different from the PLBFS, the streaming time step used at the cell interface is decoupled from the updating time step at the cell center in the present solver. Furthermore, a simplified flux reconstruction strategy is proposed to avoid complex calculations and save computing resources. Several numerical examples have been adopted to test the proposed method. The simulations of the nonlinear lid-driven cavity flow show that our method is more accurate than the original PLBFS. Results also demonstrate that the simplified method can reduce the computational time by 43%. [ABSTRACT FROM AUTHOR]

Recently, a simplified lattice Boltzmann method without evolution of distribution functions was developed. This method adopts the predictor‐corrector scheme to evolve the macroscopic variables. Unlike the original simplified method, we develop a one‐step scheme based on the resultant governing equations given by the Chapman–Enskog expansion analysis of the lattice Boltzmann equation. The proposed method abandons the predictor‐corrector scheme and only needs one step to solve the governing equations without additional intermediate implementation. As a result, the computational efficiency can be improved. In addition, the theoretical analysis demonstrates that the present method has second‐order of accuracy. To treat the boundary, the second‐order approximations for equilibrium distribution functions are employed. To validate the proposed one‐step method, several cases including the Poiseuille flow, the Womersley flow, the Taylor‐Green vortex flow, and the lid‐driven cavity flow are simulated. The numerical results agree with the analytical solutions or the reference data. And the second‐order of accuracy is ensured. Moreover, simulations also suggest that our method has good performances on the numerical stability and the computational efficiency. And the improved efficiency is no less than 30% in our tests. [ABSTRACT FROM AUTHOR]

In this work, improved simplified and highly stable lattice Boltzmann methods (SHSLBMs) are developed for incompressible flows. The SHSLBM is a newly developed scheme within the lattice Boltzmann method (LBM) framework, which utilizes the fractional step technology to resolve the governing equations recovered from lattice Boltzmann equation (LBE) and reconstructs the equations in the Lattice Boltzmann frame. By this treatment, the SHSLBM directly tracks the macroscopic variables in the evolution process rather than the distribution functions of each grid node, which greatly saves virtual memories and simplifies the implementation of physical boundary conditions. However, the Chapman–Enskog expansion analysis reveals that the SHSLBM recover the weakly compressible Navier–Stokes equations with the low Mach number assumption. Therefore, the original SHSLBM can be regarded as an artificial compressible method and may cause some undesired errors. By modifying the evolution equation for the density distribution function, the improved SHSLBMs can eliminate the compressible effects. The incompressible SHSLBMs are compared with the original SHSLBM in terms of accuracy and stability by simulating several two-dimensional steady and unsteady incompressible flow problems, and the results demonstrate that the present SHSLBMs ensure the second order of accuracy and can reduce the compressible effects efficiently, especially for the incompressible flows with large pressure gradients. We then extended the present SHSLBMs to study the more complicated two-dimensional lid-driven flow and found that the present results are in good agreement with available benchmark results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]