Development of lattice boltzmann flux solvers and their applications

Abstract

Firstly, four consistent lattice Boltzmann flux solvers (LBFSs) have been proposed respectively for simulating isothermal, thermal, axisymmetric and multiphase flows. The LBFSs are finite volume schemes for direct updating the macroscopic flow variables by solving the conservative governing equations recovered by the LBE models. The fluxes of the LBFSs are modeled at each interface by local reconstruction of the standard LBE solutions, where the theoretical connections between the macroscopic fluxes and the microscopic density and/or internal energy distribution functions are utilized. Additional source terms, including external forces and those of axisymmetric effects, are conveniently taken into account by either adding them directly into the governing equations or applying a fractional-step approach. The proposed solvers have been validated by simulating a variety of 2D and 3D flows. Numerical simulations have verified that the LBFSs not only successfully eliminate the drawbacks of LBE solvers, such as mesh uniformity, tie-up between time step and mesh spacing, limited to viscous flows and complicated implementation of boundary conditions, but also combine the advantages of the N-S solvers and LBE solvers.

The broad applications of the LBFSs have also been extended to study the complex moving boundary flow and freely falling flow problems by proposing two LBFS-based solvers respectively in the fixed Eulerian coordinates and the Arbitrary-Lagrangian-Eulerian (ALE) framework. In these two solvers, a fractional-step approach is applied to simplify the overall solution process and the immersed boundary method (IBM) is introduced to flexibly consider the boundary conditions with simplicity. Both solvers have been well validated by respectively simulating various 2D and 3D moving boundary and freely falling flows. It is noteworthy that it is the first time for the LBE-based solvers to successfully simulate flows with general freely falling objects, which seems to provide a powerful tool for solving more complicated flow-structure-interaction problems.