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Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction

Chennakesava Kadapa Orcid Logo, Wulf Dettmer Orcid Logo, Djordje Peric Orcid Logo

Journal of Fluids and Structures, Volume: 97, Start page: 103077

Swansea University Authors: Chennakesava Kadapa Orcid Logo, Wulf Dettmer Orcid Logo, Djordje Peric Orcid Logo

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DOI (Published version): 10.1016/j.jfluidstructs.2020.103077

Abstract

Stabilised mixed velocity–pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier–Stokes. In these formulations, the Newton–Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamen...

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Published in: Journal of Fluids and Structures
ISSN: 0889-9746
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54677
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spelling 2020-08-21T16:49:15.1325787 v2 54677 2020-07-09 Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction de01927f8c2c4ad9dcc034c327ac8de1 0000-0001-6092-9047 Chennakesava Kadapa Chennakesava Kadapa true false 30bb53ad906e7160e947fa01c16abf55 0000-0003-0799-4645 Wulf Dettmer Wulf Dettmer true false 9d35cb799b2542ad39140943a9a9da65 0000-0002-1112-301X Djordje Peric Djordje Peric true false 2020-07-09 MACS Stabilised mixed velocity–pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier–Stokes. In these formulations, the Newton–Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton–Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier–Stokes that preserves second-order temporal accuracy of the generalised-alpha and related schemes for both velocity and pressure fields. First, we demonstrate the second-order temporal accuracy using numerical convergence studies for an example with a manufactured solution. Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder. Towards showcasing the applicability of the proposed technique in a wider context, the inf–sup stable P2–P1 pair for the formulation without stabilisation is also considered. Finally, the resulting benefits of using the proposed scheme for fluid–structure interaction problems are illustrated using two benchmark examples in fluid-flexible structure interaction. Journal Article Journal of Fluids and Structures 97 103077 Elsevier BV 0889-9746 Incompressible Navier–Stokes, SUPG/PSPG stabilisation, Newton–Raphson scheme, Fluid–structure interaction 1 8 2020 2020-08-01 10.1016/j.jfluidstructs.2020.103077 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2020-08-21T16:49:15.1325787 2020-07-09T13:46:50.2096958 Chennakesava Kadapa 0000-0001-6092-9047 1 Wulf Dettmer 0000-0003-0799-4645 2 Djordje Peric 0000-0002-1112-301X 3 54677__17696__2f4c66c6825e4c39bee8877bb86933f6.pdf 54677.pdf 2020-07-13T13:17:52.2379693 Output 824445 application/pdf Accepted Manuscript true 2021-07-03T00:00:00.0000000 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ true English
title Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction
spellingShingle Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction
Chennakesava Kadapa
Wulf Dettmer
Djordje Peric
title_short Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction
title_full Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction
title_fullStr Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction
title_full_unstemmed Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction
title_sort Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction
author_id_str_mv de01927f8c2c4ad9dcc034c327ac8de1
30bb53ad906e7160e947fa01c16abf55
9d35cb799b2542ad39140943a9a9da65
author_id_fullname_str_mv de01927f8c2c4ad9dcc034c327ac8de1_***_Chennakesava Kadapa
30bb53ad906e7160e947fa01c16abf55_***_Wulf Dettmer
9d35cb799b2542ad39140943a9a9da65_***_Djordje Peric
author Chennakesava Kadapa
Wulf Dettmer
Djordje Peric
author2 Chennakesava Kadapa
Wulf Dettmer
Djordje Peric
format Journal article
container_title Journal of Fluids and Structures
container_volume 97
container_start_page 103077
publishDate 2020
institution Swansea University
issn 0889-9746
doi_str_mv 10.1016/j.jfluidstructs.2020.103077
publisher Elsevier BV
document_store_str 1
active_str 0
description Stabilised mixed velocity–pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier–Stokes. In these formulations, the Newton–Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton–Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier–Stokes that preserves second-order temporal accuracy of the generalised-alpha and related schemes for both velocity and pressure fields. First, we demonstrate the second-order temporal accuracy using numerical convergence studies for an example with a manufactured solution. Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder. Towards showcasing the applicability of the proposed technique in a wider context, the inf–sup stable P2–P1 pair for the formulation without stabilisation is also considered. Finally, the resulting benefits of using the proposed scheme for fluid–structure interaction problems are illustrated using two benchmark examples in fluid-flexible structure interaction.
published_date 2020-08-01T07:55:23Z
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score 11.047501

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