Numerical simulation of flow past a square obstacle with Lattice Boltzmann Method

Numerical technique Lattice Boltzmann Method (LBM) is relatively new approach based on gas kinetic theory in meso-scale. Macroscopic variables such as pressure and velocity can be determined by momentum of so called particle distribution functions which are described by Boltzmann transport equation. LBM has been extensively studied in last several decades and witnessed as capable like conventional methods for various fluid problems. LBM has its own procedure to solve fluid problems and aforementioned Boltzmann equation (LBE) used to solve fluid flow instead of Navier-Stokes equation (NSE) [1]. To reveal LBM is liable to apply fluid flow, derivation of macroscopic NSE from LBE is made under the Chapman-Enskog expansion which is a multiscale analysis by Chapman and Enskog [2]. LBM is a well-established alternative when it comes to simulate various types of fluid flows including turbulence, multicomponent, multiphase, and porous media flows across complicated geometries [3]. In civil engineering field LBM has been successfully solved free surface flow, groundwater flow and tsunami with shallow water equation. Main advantages of LBM being useful and attractive method in fluid dynamics over the classical approach to solving NSE are its remarkable conceptual simplicity, ease of implementation, predestination to massive parallel computing and straightforward implementation of geometry. In this paper, simplest form of LBM, namely LBM with Bhatnagar-Gross-Krook (BGK) collision operator, is incorporated with turbulent theory and presented for flow around simple square obstacle.