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Low-order face-based approaches for incompressible computational fluid dynamics / LUAN VIEIRA

Swansea University Author: LUAN VIEIRA

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DOI (Published version): 10.23889/SUThesis.68820

Abstract

The fast and accurate simulation of laminar and turbulent incompressible flows is crucial in science and engineering. Low-order numerical strategies, particularly finite-volume (FV) methods based on cell-centred and vertex-centred approaches, remain essential in CFD, especially in industrial settings,...

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Published: Swansea University, Wales, UK 2025
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
Supervisor: Sevilla, R., Huerta, A. & Giacomini, M.
URI: https://cronfa.swan.ac.uk/Record/cronfa68820
first_indexed 2025-02-06T17:34:50Z
last_indexed 2025-02-07T05:56:39Z
id cronfa68820
recordtype RisThesis
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However, these methods face challenges such as stabilising convective-dominated &#xFB02;ows, handling velocity-pressure coupling, and managing numerical &#xFB02;ux reconstruction on distorted and stretched grids. The face-centred &#xFB01;nite volume (FCFV) method emerges as an alternative to standard FV methods. Derived from a mixed formulation of the discontinuous Galerkin method, FCFV avoids &#xFB02;ux reconstruction at cell faces, making its accuracy and convergence nearly insensitive to grid quality. It also satis&#xFB01;es the Ladyzhenskaya-Babu&#x2C7;ska- Brezzi (LBB) condition without special treatment for velocity-pressure coupling. This work showcases the FCFV method for simulating laminar and turbulent incompressible &#xFB02;ows for the &#xFB01;rst time. The formulation is based on the Reynolds-averaged Navier-Stokes (RANS) equations coupled with the negative Spalart-Allmaras (SA) model. Three new convective stabilisations inspired by Riemann solvers are proposed, along with monolithic and staggered solution strategies for the RANS-SA system and two relaxation strategies for pseudo-time marching. A new hybrid pressure FCFV formulation is also introduced to improve the FCFV accuracy in laminar &#xFB02;ow simulations by enriching the pressure space through relaxed compressibility conditions. Both FCFV and hybrid pressure FCFV achieve &#xFB01;rst-order con- vergence of velocity, velocity gradient tensor, and pressure, accurately predicting engineering quantities such as drag and lift on structured and unstructured meshes. By avoiding gradient reconstruction, these methods are less sensitive to mesh quality, even on highly distorted grids. Numerical benchmarks for laminar and turbulent, steady and transient cases assess the performance, accuracy, and robustness of the proposed methodologies. 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spelling 2025-02-06T17:39:07.8292359 v2 68820 2025-02-06 Low-order face-based approaches for incompressible computational fluid dynamics 53118ba8e77e55452a5228efae6f2fc1 LUAN VIEIRA LUAN VIEIRA true false 2025-02-06 The fast and accurate simulation of laminar and turbulent incompressible flows is crucial in science and engineering. Low-order numerical strategies, particularly finite-volume (FV) methods based on cell-centred and vertex-centred approaches, remain essential in CFD, especially in industrial settings, due to their favourable trade-off between computational cost and accuracy. However, these methods face challenges such as stabilising convective-dominated flows, handling velocity-pressure coupling, and managing numerical flux reconstruction on distorted and stretched grids. The face-centred finite volume (FCFV) method emerges as an alternative to standard FV methods. Derived from a mixed formulation of the discontinuous Galerkin method, FCFV avoids flux reconstruction at cell faces, making its accuracy and convergence nearly insensitive to grid quality. It also satisfies the Ladyzhenskaya-Babuˇska- Brezzi (LBB) condition without special treatment for velocity-pressure coupling. This work showcases the FCFV method for simulating laminar and turbulent incompressible flows for the first time. The formulation is based on the Reynolds-averaged Navier-Stokes (RANS) equations coupled with the negative Spalart-Allmaras (SA) model. Three new convective stabilisations inspired by Riemann solvers are proposed, along with monolithic and staggered solution strategies for the RANS-SA system and two relaxation strategies for pseudo-time marching. A new hybrid pressure FCFV formulation is also introduced to improve the FCFV accuracy in laminar flow simulations by enriching the pressure space through relaxed compressibility conditions. Both FCFV and hybrid pressure FCFV achieve first-order con- vergence of velocity, velocity gradient tensor, and pressure, accurately predicting engineering quantities such as drag and lift on structured and unstructured meshes. By avoiding gradient reconstruction, these methods are less sensitive to mesh quality, even on highly distorted grids. Numerical benchmarks for laminar and turbulent, steady and transient cases assess the performance, accuracy, and robustness of the proposed methodologies. Implemented in Fortran 90, these methods lay the foundation for the integration of FCFV techniques within the CFD community. The work concludes with a detailed discussion of the Fortran 90 FCFV code implementation. E-Thesis Swansea University, Wales, UK Finite volumes, face-centred, Incompressible flows, Hybridisable discontinuous Galerkin, Sparlat-Allmaras, CFD, Fortran 90 8 1 2025 2025-01-08 10.23889/SUThesis.68820 A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information COLLEGE NANME COLLEGE CODE Swansea University Sevilla, R., Huerta, A. & Giacomini, M. Doctoral Ph.D ProTechTion European Union Horizon 2020, MCIN ProTechTion European Union Horizon 2020, MCIN 2025-02-06T17:39:07.8292359 2025-02-06T17:06:37.2309965 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering LUAN VIEIRA 1 68820__33529__67013ec3a5a540c6af5b385c062808c8.pdf 2024_Vieira_L.final.68820.pdf 2025-02-06T17:21:58.3426899 Output 40768887 application/pdf E-Thesis – open access true Copyright: The Author, Luan Malikoski Vieira, 2024 true eng
title Low-order face-based approaches for incompressible computational fluid dynamics
spellingShingle Low-order face-based approaches for incompressible computational fluid dynamics
LUAN VIEIRA
title_short Low-order face-based approaches for incompressible computational fluid dynamics
title_full Low-order face-based approaches for incompressible computational fluid dynamics
title_fullStr Low-order face-based approaches for incompressible computational fluid dynamics
title_full_unstemmed Low-order face-based approaches for incompressible computational fluid dynamics
title_sort Low-order face-based approaches for incompressible computational fluid dynamics
author_id_str_mv 53118ba8e77e55452a5228efae6f2fc1
author_id_fullname_str_mv 53118ba8e77e55452a5228efae6f2fc1_***_LUAN VIEIRA
author LUAN VIEIRA
author2 LUAN VIEIRA
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publishDate 2025
institution Swansea University
doi_str_mv 10.23889/SUThesis.68820
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
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description The fast and accurate simulation of laminar and turbulent incompressible flows is crucial in science and engineering. Low-order numerical strategies, particularly finite-volume (FV) methods based on cell-centred and vertex-centred approaches, remain essential in CFD, especially in industrial settings, due to their favourable trade-off between computational cost and accuracy. However, these methods face challenges such as stabilising convective-dominated flows, handling velocity-pressure coupling, and managing numerical flux reconstruction on distorted and stretched grids. The face-centred finite volume (FCFV) method emerges as an alternative to standard FV methods. Derived from a mixed formulation of the discontinuous Galerkin method, FCFV avoids flux reconstruction at cell faces, making its accuracy and convergence nearly insensitive to grid quality. It also satisfies the Ladyzhenskaya-Babuˇska- Brezzi (LBB) condition without special treatment for velocity-pressure coupling. This work showcases the FCFV method for simulating laminar and turbulent incompressible flows for the first time. The formulation is based on the Reynolds-averaged Navier-Stokes (RANS) equations coupled with the negative Spalart-Allmaras (SA) model. Three new convective stabilisations inspired by Riemann solvers are proposed, along with monolithic and staggered solution strategies for the RANS-SA system and two relaxation strategies for pseudo-time marching. A new hybrid pressure FCFV formulation is also introduced to improve the FCFV accuracy in laminar flow simulations by enriching the pressure space through relaxed compressibility conditions. Both FCFV and hybrid pressure FCFV achieve first-order con- vergence of velocity, velocity gradient tensor, and pressure, accurately predicting engineering quantities such as drag and lift on structured and unstructured meshes. By avoiding gradient reconstruction, these methods are less sensitive to mesh quality, even on highly distorted grids. Numerical benchmarks for laminar and turbulent, steady and transient cases assess the performance, accuracy, and robustness of the proposed methodologies. Implemented in Fortran 90, these methods lay the foundation for the integration of FCFV techniques within the CFD community. The work concludes with a detailed discussion of the Fortran 90 FCFV code implementation.
published_date 2025-01-08T05:25:18Z
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score 11.089572

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