Slip velocity of lattice Boltzmann simulation using bounce-back boundary scheme

TL;DR

This paper investigates the cause of non-physical slip velocities in lattice Boltzmann simulations with bounce-back boundary schemes, revealing that the issue stems from undefined boundary conditions for certain discrete velocities and can be mitigated by proper velocity specification.

Contribution

The study identifies the root cause of slip velocity issues in bounce-back schemes and demonstrates a simple solution for basic geometries, advancing understanding of boundary treatment in lattice Boltzmann methods.

Findings

Non-physical slip is caused by undefined boundary conditions for parallel velocities.

The issue is independent of the single-relaxation-time scheme.

Proper velocity specification can eliminate slip in simple geometries.

Abstract

In this work we investigate the issue of non-physical slip at wall of lattice Boltzmann simulations with the bounce-back boundary scheme. By comparing the analytical solution of two lattice models with four and nine discrete velocities for the force-driven Poiseuille flow, we are able to reveal the exact mechanism causing the issue. In fact, no boundary condition is defined by the bounce-back scheme for the the discrete velocities parallel to wall. Other factors, such as initial conditions and inlet and outlet boundary conditions, can play the role and induce the non-physical slip velocity. Therefore, the issue is not related to the single-relaxation-time scheme. Naturally the key for resolving it is to specify the definition for these velocities. Through a lid-driven cavity flow, we show that the solution can be as easy as no extra effort required for simple geometries, although further study is necessary for complex geometries.