Numerical Simulation Of Flow Around A Square Cylinder Based On The Method Of Pseudo-Compressibility

During the recent years, a great deal of effort has been made to develop numerical methods for simulating the fluid phenomena, which has been the goals of the fluid researchers. Dued to the importance of the flow around the blunt bodies both in the theoretical study and in practice application, the two-dimensional numerical simulation for flow around square cylinder is performed, using pseudo-compressibility method and Finite Volume Method (FVM) in the paper.Based on the CFD theories and routine numerical methods, the incompressible N-S equations are considered to be the governing equations in the paper. At the same time, in order to acquire extensive adaptability of the program, the dimensionless form of the N-S equations was adopted. Because of a few problems in some kinds of pressure-speed coupling algorithms, pseudo-compressibility method is applied to solve the incompressible N-S, so as to simplify the solving process and the designing process of the program. In addition, corresponding measures of initial condition and boundary condition are presented.To solve fluid problem, differential equations must be discretized in the computational field. According to the character of the object, the direct method is implemented to build uniformly rectangle grid, and at the same time, pressure and velocity are collocated at the same grid. In the paper, involved grid elements of FVM are setted: CV(Cell-Vertice) in joint and VC(vertex-centered) in volume, and uniform naming regulation of geometrical elements is made. Then, FVM is adopted to discretize the differential equations. The discretization process is deduced in detail, and the final iteration formula is given. In the discretization equations, higher order upwind differencing scheme is introduced into the calculation of the convection flux, whereas as for diffusion term, a central differencing scheme is taken into account. To overcome thedisadvantages of pseudo-compressibility algorithm, four-order artificial dissipation term is added to the right of the differential equation, and the recommended formula is offered for the choice of the artificial dissipation coefficient ε.In addition, in order to solve the differencing equations, feasible project is presented to deal with the first and second boundary conditions. Finally, Jacobi interation method is selected for the solution of the equation systems.According to the theory above, several programs are developed to solve the questions and show the results of the flow. With the computing program, flow around the square cylinder is resolved at first, and the period of laminar flow is simulated successfully. During the period of vortex street (Re=100), the periodically evolutionary phenomena of the flow behind the square cylinder can be seen. Then, the program is used to simulate the flow across the backward-step, and the conclusion is testified that the circumfluence length is related to the Reyonlds number. Finally, numerical experiments are carried out to weigh the influence of the artificial dissipation coefficient a and the pseudo-compressibility coefficient ε.Although the numerical results have been obtained in the paper, it can't be considered as successfully as expected, because of the limitation of the means and time and so on. More research should be done to seek for better results. Finally, both experiences and lessons from the present work are discussed, which should be paid more attention to in the future work.