A systematic study for determining the optimal relaxation time in the lattice Boltzmann method at low Reynolds numbers

Abstract

In the lattice Boltzmann method (LBM), the relaxation time plays a significant role in the accuracy of simulation. However, there has been little attention directed toward evaluating the optimal relaxation time in literature. This paper proposes a systematic approach for the determination of the optimal relaxation time, particularly for very-low Reynolds (Re) number flows as analogues for blood flow in micro-vessels. The LBM with D2Q9 lattice model is used to simulate Poiseuille flow in a micro-channel and its accuracy is verified against the analytical solution. It was found that for a given number of grid points in the y-direction, the value of optimal relaxation time predicted analytically differs from that obtained from the numerical solutions. This indicates that the analytical relaxation time should be corrected when used in the LBM code.

Keywords

• LBM
• Optimal relaxation time
• Poiseuille flow
• Micro-channel
• Low Reynolds number