Numerical solution of the momentum equations in unsteady incompressible flow

A general method is developed for the solution of time-dependent unsteady incompressible flow problems using standard finite-difference techniques. The method utilizes a velocity correction which ensures mass conservation, but momentum conservation is satisfied only approximately. The method is applied to problems of three-dimensional periodic nonviscous flow inside a cylinder and two-dimensional transient viscous free convection. Tests of stability and accuracy show that this method gives satisfactory results, although the efficiency of the method depends on the efficiency of the marching algorithm.