Finite element solution for advection and natural convection flows

Abstract

A new equal order velocity--pressure finite element procedure is presented for the calculation of 2-D viscous, incompressible flows of a recirculating nature. As in the finite difference procedures, velocity and pressure e uncoupled and the equations are solved one after the other. In this splitting-up method, an auxilary velocity field is computed first, which accounts for all contributions to the acceleration, except pressure, and satisfies the velocity boundary conditions. Then, the final velocities are evaluated by adding to the auxilary velocities pressure contributions which are computed to satisfy the continuity equation. The effectiveness is illustrated via example problems of 2-D advection and natural convection flows.