A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows - Perumal Nithiarasu (International Journal of Numerical Methods for Heat & Fluid Flow, 2016)
In the present work, a novel dual time stepping approach is applied to a quasi-implicit (QI) fractionalstep method and its performance is assessed against the classical versions of the quasi-implicit procedurefor the solution of incompressible Navier-Stokes equations. In the proposed dual time stepping method,a local time stepping algorithm is utilised to accelerate the solution to steady state, while the transientsolution is recovered through the use of a backward dierence formula (BDF). It is demonstrated that,unlike the classical fractional step method, the temporal convergence rate of the proposed method de-pends solely upon the choice of the BDF. While additional stabilisation is the prerequisite for obtaininghigher order accuracy in the standard QI methods, the proposed dual time stepping approach completelyeliminates this requirement. In addition, the dual time stepping approach proposed achieves the correctformal accuracy in time for both velocity and pressure. It is also demonstrated that a time accuracybeyond second order for both pressure and velocity is possible. In summary, the proposed dual timeapproach to QI methods simplies the algorithm, accelerates solution and achieves a higher order timeaccuracy.