In this paper, simulation studies are carried for flow over circular cylinder(s) to analyze the wake dynamics, drag, and lift. The numerical problems discussed are: (a) two-dimensional, laminar, and unsteady flow past a single circular cylinder, (b) flow past two circular cylinders of different diameters arranged in Big-Small (BSA) or Small-Big (SBA) arrangement and identical cylinders placed in tandem arrangement in a channel, and (c) flow past moving single circular cylinder with a constant velocity in a stationary flow. The simulations are carried out using the lattice Boltzmann method (LBM) employing multiple-relaxation time (MRT) collision model. For the tandem arrangement, the effect of spacing ratio, cylinder size on the wake dynamics, and mean drag coefficient are discussed. The transition from steady flow to a periodic vortex shedding regime where one can witness the von-Karman vortex street is discussed. Further, to extend the work to study the moving particles in a flow, it is important to evaluate the hydrodynamic forces. The computational nodes are uncovered when the solid moves from solid to fluid. For this, the momentum exchange method and refilling algorithm are used to evaluate the force in LBM for fluid flow-particle interactions. These approaches are translated in the computer code and tested for the movement of circular cylinders in a channel.