Abstract: The first-order time splitting method is used to discretize the Navier-Stokes equations with primitive variables and a conjugate gradient method is used to decouple the variables.The resulted Laplace equations, Possion equations and Helmhotz equations are solved by using Boundary Integral Method and thus a boundary integral formulation for viscous Navier-Stokes equation is established for the first time.The numerical results for the steady and unsteady viscous flow aroulld cylindical body show the method de...