In this paper, a viscous flow simulation is presented using the Lattice Boltzmann Equation (LBE). A finite volume approach is adapted to discretize the LBE on a cell-centered, arbitrary shaped, rectangular tessellation. The formulation includes upwind scheme and high order descretization schemes for the flux term and collision operator respectively. A consistent open and solid boundary treatment according to cell-centered scheme also addressed, which resulted in a wider domain of stability and faster convergence. Validation of the results is conducted by symmetric sudden expansion. The results are compared with reliable analytical or experimental results, indicating the accuracy and robustness' of the proposed method for analyzing different flows of the interest.