Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations

TL;DR

This paper introduces a lattice Boltzmann numerical method for solving volume-averaged Navier-Stokes equations, demonstrating its accuracy and efficiency in modeling fluid flow through porous media.

Contribution

A novel lattice Boltzmann approach with modified equilibrium and forcing terms for volume-averaged Navier-Stokes equations, enabling explicit and parallelizable simulations.

Findings

Accurately reproduces linear and nonlinear drag effects in porous media.

Demonstrates advantages over traditional numerical methods in efficiency and parallelism.

Validates the model through numerical simulations.

Abstract

A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.