A control-volume finite-element method (CVFEM) for unsteady, incompressible, viscous fluid flows

A control-volume finite-element method (CVFEM), to stimulate unsteady, incompressible, and viscous fluid flows, using nine-noded quadrilateral elements, has been developed. The Navier-Stokes equations in primitive variables u-nu -p are the mathematical model of the flows. A technique of upwind, known as MAW, Mass-Weighted Interpolation, was extended for the finite element employed in this work. The set of nonlinear partial differential equations was integrated, and after using interpolation functions and time discretization, the algebraic system of equations was solved by using the frontal method of solution. Results obtained for some benchmark problems compared favorably with available results from the literature.