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A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows / Rhodri LT Bevan, Etienne Boileau, Raoul van Loon, R.W. Lewis, Perumal Nithiarasu

International Journal of Numerical Methods for Heat & Fluid Flow, Volume: 26, Issue: 3/4, Pages: 595 - 623

Swansea University Authors: Raoul van Loon, Perumal Nithiarasu

DOI (Published version): 10.1108/HFF-06-2015-0233

Abstract

The present review describes and analyses a class of finite element fractional step methodsfor solving the incompressible Navier-Stokes equations. Our objective is not to reproduce the extensivecontributions on the subject, but to report on our long-term experience with and provide a unified overvie...

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Published in: International Journal of Numerical Methods for Heat & Fluid Flow
Published: 2016
URI: https://cronfa.swan.ac.uk/Record/cronfa25294
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spelling 2020-05-22T18:55:33.5650042 v2 25294 2016-01-02 A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows 880b30f90841a022f1e5bac32fb12193 0000-0003-3581-5827 Raoul van Loon Raoul van Loon true false 3b28bf59358fc2b9bd9a46897dbfc92d 0000-0002-4901-2980 Perumal Nithiarasu Perumal Nithiarasu true false 2016-01-02 MEDE The present review describes and analyses a class of finite element fractional step methodsfor solving the incompressible Navier-Stokes equations. Our objective is not to reproduce the extensivecontributions on the subject, but to report on our long-term experience with and provide a unified overviewof a particular approach: the characteristic based split method. Three procedures, the semi-implicit, quasi-implicit and fully-explicit, are studied and compared. This work provides a thorough assessment of theaccuracy and efficiency of these schemes, both for a first and second order pressure split. In transientproblems, the quasi-implicit form significantly outperforms the fully-explicit approach. The second order(pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully-explicit method, utilising artificial compressibility and apseudo time stepping procedure, requires no second order fractional split to achieve second order or higheraccuracy. While the fully-explicit form is efficient for steady state problems, due to its ability to handle localtime stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations. Journal Article International Journal of Numerical Methods for Heat & Fluid Flow 26 3/4 595 623 20 5 2016 2016-05-20 10.1108/HFF-06-2015-0233 COLLEGE NANME Biomedical Engineering COLLEGE CODE MEDE Swansea University Institution 2020-05-22T18:55:33.5650042 2016-01-02T12:07:28.0490457 College of Engineering Engineering Rhodri LT Bevan 1 Etienne Boileau 2 Raoul van Loon 0000-0003-3581-5827 3 R.W. Lewis 4 Perumal Nithiarasu 0000-0002-4901-2980 5 0025294-02012016152405.pdf ijnmhffv3.pdf 2016-01-02T12:16:33.0530000 Output 7805471 application/pdf Accepted Manuscript true 2016-01-02T00:00:00.0000000 true
title A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
spellingShingle A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
Raoul, van Loon
Perumal, Nithiarasu
title_short A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
title_full A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
title_fullStr A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
title_full_unstemmed A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
title_sort A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows
author_id_str_mv 880b30f90841a022f1e5bac32fb12193
3b28bf59358fc2b9bd9a46897dbfc92d
author_id_fullname_str_mv 880b30f90841a022f1e5bac32fb12193_***_Raoul, van Loon
3b28bf59358fc2b9bd9a46897dbfc92d_***_Perumal, Nithiarasu
author Raoul, van Loon
Perumal, Nithiarasu
author2 Rhodri LT Bevan
Etienne Boileau
Raoul van Loon
R.W. Lewis
Perumal Nithiarasu
format Journal article
container_title International Journal of Numerical Methods for Heat & Fluid Flow
container_volume 26
container_issue 3/4
container_start_page 595
publishDate 2016
institution Swansea University
doi_str_mv 10.1108/HFF-06-2015-0233
college_str College of Engineering
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hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description The present review describes and analyses a class of finite element fractional step methodsfor solving the incompressible Navier-Stokes equations. Our objective is not to reproduce the extensivecontributions on the subject, but to report on our long-term experience with and provide a unified overviewof a particular approach: the characteristic based split method. Three procedures, the semi-implicit, quasi-implicit and fully-explicit, are studied and compared. This work provides a thorough assessment of theaccuracy and efficiency of these schemes, both for a first and second order pressure split. In transientproblems, the quasi-implicit form significantly outperforms the fully-explicit approach. The second order(pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully-explicit method, utilising artificial compressibility and apseudo time stepping procedure, requires no second order fractional split to achieve second order or higheraccuracy. While the fully-explicit form is efficient for steady state problems, due to its ability to handle localtime stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.
published_date 2016-05-20T03:41:59Z
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