A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows

Abstract

Purpose

In the present work, a novel dual time stepping approach is applied to a quasi-implicit (QI) fractional step method and its performance is assessed against the classical versions of the QI procedure for the solution of incompressible Navier-Stokes equations. The paper aims to discuss these issues.

Design/methodology/approach

In the proposed method, a local time stepping algorithm is utilised to accelerate the solution to steady state, while the transient solution is recovered through the use of a dual time step. It is demonstrated that, unlike the classical fractional step method, the temporal convergence rate of the proposed method depends solely upon the choice of the time discretisation.

Findings

While additional stabilisation is the prerequisite for obtaining higher order accuracy in the standard QI methods, the proposed dual time stepping approach completely eliminates this requirement. In addition, the dual time stepping approach proposed achieves the correct formal accuracy in time for both velocity and pressure. It is also demonstrated that a time accuracy beyond second order for both pressure and velocity is possible. In summary, the proposed dual time approach to QI methods simplifies the algorithm, accelerates solution and achieves a higher order time accuracy.

Originality/value

The dual time stepping removed first order pressure error.

Citation

Bevan, R.L. and Nithiarasu, P. (2016), "A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 2, pp. 556-570. https://doi.org/10.1108/HFF-03-2015-0090