Boundary integral equation formulations for unsteady incompressible viscous fluid flow by time-differencing

Boundary integral equations for the flow of an incompressible viscous fluid in two and three dimensions are presented. Flow velocity and pressure are taken as field unknowns. Time derivatives in the Navier-Stokes equations are approximated by one-step finite differences. The semidiscretized differential equations are transformed into the integral equations using the weighted-residual method. Fundamental solutions of linearized equations are used as the weight functions. Boundary collocations using linear boundary elements are considered for discretization of the integral equations.