Simulation of vortex shedding around cylinders by immersed boundary-lattice Boltzmann flux solver

The hydrodynamic response accompanied with vortex shedding around circular cylinders plays a pivotal role in ocean engineering, and the numerical simulation is an essential and efficient way. The computational domain is usually in large scale for this kind of problem, and the details of flow field surrounding structures are necessary to be observed as they play key influence. Comparing with popular numerical methods for fluids such as the Navier-Stokes (N-S) solver and the lattice Boltzmann method (LBM), to some extent, the lattice Boltzmann flux solver (LBFS) inherits their advantages and removes the limitations so that the accuracy and efficiency are both ensured. In this work, the immersed boundary-lattice Boltzmann flux solver (IB-LBFS) with implicit velocity correction is implemented to simulate vortex shedding around circular cylinders. Firstly, the simulation of flow past an isolated stationary cylinder is carried out as the validation of the IB-LBFS. After that, the phenomena of flow past two stationary cylinders in two kinds of arrangements are simulated with respective spacing ratios and Reynolds numbers. The instantaneous contours of vorticity are shown to illustrate the vortex shedding, and the hydrodynamic parameters such as the drag coefficient, the lift coefficient, and the Strouhal number are given. Through comparing with previous literatures, it can be seen that the IB-LBFS is reliable and has sufficient accuracy so that it can represent the details of the flow field, for example the beat phenomenon, in this simulation, which indicates its wide application for fluid-structure interaction problems in ocean engineering.