On the dissipation mechanism of lattice Boltzmann method when modeling 1-d and 2-d water hammer flows

Abstract

This paper uses the multiple relaxation times lattice Boltzmann method (LBM) to model acoustic wave propagation in water-filled conduits (i.e. water hammer applications). The LBM scheme is validated by solving some classical water hammer (WH) numerical tests in one-dimensional and two-dimensional cases. In addition, this work discusses the accuracy, stability and robustness of LBM when solving high frequency (i.e. radial modes are excited) acoustic waves in water-filled pipes. The results are compared with a high order finite volume scheme based on Riemann Solver. The results show that LBM is capable to model WH applications with high accuracy and performance at low frequency cases; however, it loses stability and performance for high frequency (HF) cases. It is discussed that this is due to the neglected high order terms of the equivalent macroscopic equations considered for LB numerical formulation.