High-order finite-volume scheme with anisotropic adaptive mesh refinement

Efficient inexact newton method for steady three-dimensional flows

L. Freret, C. P.T. Groth, T. B. Nguyen, H. De Sterck

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch

Abstract

A high-order finite-volume method with anisotropic adaptive mesh refinement (AMR) is combined with a parallel inexact Newton method integration scheme and described for the solution of compressible fluid flows governed by Euler and Navier-Stokes equations on three-dimensional multi-block body-fitted hexahedral meshes. The proposed approach combines a family of robust and accurate high-order central essentially non-oscillatory (CENO) spatial discretization schemes with a scalable and efficient Newton-Krylov-Schwarz (NKS) algorithm and a block-based anisotropic AMR. The CENO scheme is based on a hybrid solution reconstruction procedure that provides high-order accuracy in smooth regions (even for smooth extrema) and non-oscillatory transitions at discontinuities. The implicit time stepping scheme is based on Newton’s method where the set of linear systems are solved using the generalized minimal residual (GMRES) algorithm preconditioned by a domain-based additive Schwarz technique. The latter uses the domain decomposition provided by the block-based AMR scheme leading to a fully parallel implicit approach with an efficient scalability of the overall scheme. The anisotropic AMR method is based on a binary tree and hierarchical data structure to permit local anisotropic refinement of the grid in preferred directions as directed by appropriately specified physics-based refinement criteria. Application and numerical results will be discussed for several steady inviscid and viscous problems and the computational performance of the overall scheme is demonstrated for a range of fluid flows.

Original languageEnglish
Title of host publication23rd AIAA Computational Fluid Dynamics Conference, 2017
Place of PublicationReston VA USA
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
Number of pages14
ISBN (Print)9781624105067
DOIs
Publication statusPublished - 2017
EventAIAA Computational Fluid Dynamics Conference, 2017 - Denver, United States of America
Duration: 5 Jun 20179 Jun 2017
Conference number: 23rd
https://arc.aiaa.org/doi/book/10.2514/MCFD17

Conference

ConferenceAIAA Computational Fluid Dynamics Conference, 2017
Abbreviated titleAIAA 2017
CountryUnited States of America
CityDenver
Period5/06/179/06/17
Internet address

Cite this

Freret, L., Groth, C. P. T., Nguyen, T. B., & De Sterck, H. (2017). High-order finite-volume scheme with anisotropic adaptive mesh refinement: Efficient inexact newton method for steady three-dimensional flows. In 23rd AIAA Computational Fluid Dynamics Conference, 2017 Reston VA USA: American Institute of Aeronautics and Astronautics Inc, AIAA. https://doi.org/10.2514/6.2017-3297
Freret, L. ; Groth, C. P.T. ; Nguyen, T. B. ; De Sterck, H. / High-order finite-volume scheme with anisotropic adaptive mesh refinement : Efficient inexact newton method for steady three-dimensional flows. 23rd AIAA Computational Fluid Dynamics Conference, 2017. Reston VA USA : American Institute of Aeronautics and Astronautics Inc, AIAA, 2017.
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abstract = "A high-order finite-volume method with anisotropic adaptive mesh refinement (AMR) is combined with a parallel inexact Newton method integration scheme and described for the solution of compressible fluid flows governed by Euler and Navier-Stokes equations on three-dimensional multi-block body-fitted hexahedral meshes. The proposed approach combines a family of robust and accurate high-order central essentially non-oscillatory (CENO) spatial discretization schemes with a scalable and efficient Newton-Krylov-Schwarz (NKS) algorithm and a block-based anisotropic AMR. The CENO scheme is based on a hybrid solution reconstruction procedure that provides high-order accuracy in smooth regions (even for smooth extrema) and non-oscillatory transitions at discontinuities. The implicit time stepping scheme is based on Newton’s method where the set of linear systems are solved using the generalized minimal residual (GMRES) algorithm preconditioned by a domain-based additive Schwarz technique. The latter uses the domain decomposition provided by the block-based AMR scheme leading to a fully parallel implicit approach with an efficient scalability of the overall scheme. The anisotropic AMR method is based on a binary tree and hierarchical data structure to permit local anisotropic refinement of the grid in preferred directions as directed by appropriately specified physics-based refinement criteria. Application and numerical results will be discussed for several steady inviscid and viscous problems and the computational performance of the overall scheme is demonstrated for a range of fluid flows.",
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Freret, L, Groth, CPT, Nguyen, TB & De Sterck, H 2017, High-order finite-volume scheme with anisotropic adaptive mesh refinement: Efficient inexact newton method for steady three-dimensional flows. in 23rd AIAA Computational Fluid Dynamics Conference, 2017. American Institute of Aeronautics and Astronautics Inc, AIAA, Reston VA USA, AIAA Computational Fluid Dynamics Conference, 2017, Denver, United States of America, 5/06/17. https://doi.org/10.2514/6.2017-3297

High-order finite-volume scheme with anisotropic adaptive mesh refinement : Efficient inexact newton method for steady three-dimensional flows. / Freret, L.; Groth, C. P.T.; Nguyen, T. B.; De Sterck, H.

23rd AIAA Computational Fluid Dynamics Conference, 2017. Reston VA USA : American Institute of Aeronautics and Astronautics Inc, AIAA, 2017.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch

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AB - A high-order finite-volume method with anisotropic adaptive mesh refinement (AMR) is combined with a parallel inexact Newton method integration scheme and described for the solution of compressible fluid flows governed by Euler and Navier-Stokes equations on three-dimensional multi-block body-fitted hexahedral meshes. The proposed approach combines a family of robust and accurate high-order central essentially non-oscillatory (CENO) spatial discretization schemes with a scalable and efficient Newton-Krylov-Schwarz (NKS) algorithm and a block-based anisotropic AMR. The CENO scheme is based on a hybrid solution reconstruction procedure that provides high-order accuracy in smooth regions (even for smooth extrema) and non-oscillatory transitions at discontinuities. The implicit time stepping scheme is based on Newton’s method where the set of linear systems are solved using the generalized minimal residual (GMRES) algorithm preconditioned by a domain-based additive Schwarz technique. The latter uses the domain decomposition provided by the block-based AMR scheme leading to a fully parallel implicit approach with an efficient scalability of the overall scheme. The anisotropic AMR method is based on a binary tree and hierarchical data structure to permit local anisotropic refinement of the grid in preferred directions as directed by appropriately specified physics-based refinement criteria. Application and numerical results will be discussed for several steady inviscid and viscous problems and the computational performance of the overall scheme is demonstrated for a range of fluid flows.

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SN - 9781624105067

BT - 23rd AIAA Computational Fluid Dynamics Conference, 2017

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

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Freret L, Groth CPT, Nguyen TB, De Sterck H. High-order finite-volume scheme with anisotropic adaptive mesh refinement: Efficient inexact newton method for steady three-dimensional flows. In 23rd AIAA Computational Fluid Dynamics Conference, 2017. Reston VA USA: American Institute of Aeronautics and Astronautics Inc, AIAA. 2017 https://doi.org/10.2514/6.2017-3297