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

Rhodri LT Bevan, P Nithiarasu, Perumal Nithiarasu Orcid Logo

International Journal of Numerical Methods for Heat & Fluid Flow, Volume: 26, Issue: 2, Pages: 556 - 570

Swansea University Author: Perumal Nithiarasu Orcid Logo

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DOI (Published version): 10.1108/HFF-03-2015-0090

Abstract

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 stepp...

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Published in: International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa25293
first_indexed 2016-01-03T01:55:53Z
last_indexed 2018-02-09T05:05:59Z
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spelling 2017-02-20T09:17:39.5390139 v2 25293 2016-01-02 A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows 3b28bf59358fc2b9bd9a46897dbfc92d 0000-0002-4901-2980 Perumal Nithiarasu Perumal Nithiarasu true false 2016-01-02 ACEM 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. Journal Article International Journal of Numerical Methods for Heat & Fluid Flow 26 2 556 570 0961-5539 quasi-implicit; fractional step; dual time stepping; temporal accuracy; incompressible flow, finite element method 29 2 2016 2016-02-29 10.1108/HFF-03-2015-0090 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2017-02-20T09:17:39.5390139 2016-01-02T11:51:18.6744318 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Rhodri LT Bevan 1 P Nithiarasu 2 Perumal Nithiarasu 0000-0002-4901-2980 3
title A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows
spellingShingle A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows
Perumal Nithiarasu
title_short A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows
title_full A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows
title_fullStr A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows
title_full_unstemmed A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows
title_sort A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows
author_id_str_mv 3b28bf59358fc2b9bd9a46897dbfc92d
author_id_fullname_str_mv 3b28bf59358fc2b9bd9a46897dbfc92d_***_Perumal Nithiarasu
author Perumal Nithiarasu
author2 Rhodri LT Bevan
P Nithiarasu
Perumal Nithiarasu
format Journal article
container_title International Journal of Numerical Methods for Heat & Fluid Flow
container_volume 26
container_issue 2
container_start_page 556
publishDate 2016
institution Swansea University
issn 0961-5539
doi_str_mv 10.1108/HFF-03-2015-0090
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 0
active_str 0
description 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.
published_date 2016-02-29T18:49:15Z
_version_ 1821341862842073088
score 11.04748

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