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


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
Number of pages14
ISBN (Print)9781624105067
Publication statusPublished - 2017
EventAIAA Computational Fluid Dynamics Conference, 2017 - Denver, United States of America
Duration: 5 Jun 20179 Jun 2017
Conference number: 23rd


ConferenceAIAA Computational Fluid Dynamics Conference, 2017
Abbreviated titleAIAA 2017
Country/TerritoryUnited States of America
Internet address

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