A high-order finite-volume method with anisotropic AMR for ideal MHD flows

L. Freret, L. Ivan, H. De Sterck, C. P T Groth

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

7 Citations (Scopus)


A high-order central essentially non-oscillatory (CENO) finite-volume scheme combined with a block-based anisotropic adaptive mesh refinement (AMR) algorithm is proposed for the solution of the ideal magnetohydrodynamics (MHD) equations. A generalized Lagrange multiplier (GLM) divergence correction technique is applied to achieve numerically- divergent free magnetic fields while preserving high-order accuracy. The cell-centered CENO method uses a hybrid reconstruction approach based on a fixed central stencil. Smooth and fully resolved solution data is interpolated using an unlimited high-order k- exact reconstruction. In cells deemed to have under-resolved/discontinuous solution con- tent based on a smoothness indicator, the high-order reconstruction reverts to a lower-order limited linear approach. The high-order CENO finite-volume scheme is implemented with fourth-order spatial accuracy within a flexible multi-block hexahedral grid framework. Parallel implementation and local anisotropic grid adaptivity are achieved by using a hierarchi- cal block-based domain decomposition strategy in which the connectivity and refinement history of grid blocks are tracked using a binary tree data structure. Physics-based refinement criteria are used for directing the mesh refinement. Numerical results, including solution-driven anisotropic refinement of cubed-sphere grids are presented to demonstrate the accuracy and efficiency of the proposed high-order solution method.

Original languageEnglish
Title of host publicationAIAA SciTech Forum
Subtitle of host publication55th AIAA Aerospace Sciences Meeting
Place of PublicationUSA
PublisherAmerican Institute of Aeronautics and Astronautics
Number of pages18
ISBN (Electronic)9781624104473
Publication statusPublished - 2017
EventAIAA Aerospace Sciences Meeting 2017 - Grapevine, United States of America
Duration: 9 Jan 201713 Jan 2017
Conference number: 55th


ConferenceAIAA Aerospace Sciences Meeting 2017
Country/TerritoryUnited States of America
Internet address

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