An analysis of the time integration algorithms for the finite element solutions of incompressible Navier-Stokes equations based on a stabilised formulation

摘要

This work is concerned with the analysis of time integration procedures for the stabilised finite element formulation of unsteady incompressible fluid flows governed by the Navier-Stokes equations. The stabilisation technique is com- bined with several different implicit time integration procedures including both finite difference and finite element schemes. Particular attention is given to the generalised-α method and the linear discontinuous in time finite element scheme. The time integration schemes are first applied to two model problems, represented by a first order differential equation in time and the one dimensional advection-diffusion equation, and subjected to a detailed mathematical -analysis based on the Fourier series expansion. In order to establish" the accuracy and efficiency of the time integration schemes for the Navier-Stokes equations, a detailed computational study is performed of two standard numerical examples: unsteady flow around a cylinder and flow across a backward facing step. It is concluded that the semi-discrete generalised-α method provides a viable alternative to the more sophisticated and expensive space-time methods for simulations of unsteady flows of incompressible fluids governed by the Navier-Stokes equations.