Generalized bounce back boundary condition for the nine velocities two-dimensional lattice Boltzmann scheme

TL;DR

This paper develops a generalized bounce back boundary condition for the two-dimensional nine velocities lattice Boltzmann scheme, improving accuracy and reducing spurious effects through parameter optimization and validation.

Contribution

It introduces a new generalized bounce back scheme with fewer parameters, eliminating first order spurious density terms, and validates its effectiveness in flow simulations.

Findings

Exact up to second order for specific parameters

Accurate simulation of Poiseuille flow

Validated boundary value expansion in test case

Abstract

In a previous work, we have proposed a method for the analysis of the bounce back boundary condition with the Taylor expansion method in the linear case. In this work two new schemes of modified bounce back are proposed. The first one is based on the expansion of the iteration of the internal scheme of the lattice Boltzmann method. The analysis puts in evidence some defects and a generalized version is proposed with a set of essentially four possible parameters to adjust. We propose to reduce this number to two with the elimination of spurious density first order terms. Thus a new scheme for bounce back is found exact up to second order and allows an accurate simulation of the Poiseuille flow for a specific combination of the relaxation and boundary coefficients. We have validated the general expansion of the value in the first cell in terms of given values on the boundary for a stationary "accordion" test case.