A transient solution method for the finite element incompressible Navier‐Stokes equations

Abstract

Abstract A numerical procedure for solving the time‐dependent, incompressible Navier‐Stokes equations is presented. The present method is based on a set of finite element equations of the primitive variable formulation, and a direct time integration method which has unique features in its formulation as well as in its evaluation of the contribution of external functions. Particular processes regarding the continuity conditions and the boundary conditions lead to a set of non‐linear recurrence equations which represent evolution of the velocities and the pressures under the incompressibility constraint. An iteration process as to the non‐linear convective terms is performed until the convergence is achieved in every integration step. Excessively artificial techniques are not introduced into the present solution procedure. Numerical examples with vortex shedding behind a rectangular cylinder are presented to illustrate the features of the proposed method. The calculated results are compared with experimental data and visualized flow fields in literature.