A consistent generalized model-based lattice Boltzmann flux solver for incompressible porous flows

Abstract

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%.