A heuristic curved-boundary treatment in lattice Boltzmann method

State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology - Wuhan 430074, China

Received: 3 August 2010
Accepted: 17 November 2010

Abstract

Curved boundary treatments provide a way to improve the computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann (LB) simulations. However, the existing methods either require at least two or three fluid nodes between nearby solid surfaces, a condition that cannot be satisfied in the scenarios where only one fluid node is available, or break the mass conservation at the solid-wall surface that may result in serious numerical instability. Until now there is no boundary treatment that can remedy these two disadvantages with second-order accuracy at the same time. In this letter, we develop a heuristic curved-boundary treatment for the LB method from the viewpoint of surface chemistry. This simple scheme can overcome the aforementioned disadvantages synchronously. The numerical experiments show that the present scheme gives second-order accuracy. Moreover, the midway bounce-back scheme and the non-equilibrium extrapolation scheme for boundary treatment both can be recovered from the present scheme.