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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 1/2019

12.10.2018

High-Order Finite-Volume Method with Block-Based AMR for Magnetohydrodynamics Flows

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

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2019

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Abstract

A high-order central essentially non-oscillatory (CENO) finite volume scheme combined with a block-based adaptive mesh refinement (AMR) algorithm is proposed for the solution of the ideal magnetohydrodynamics equations. The high-order CENO finite-volume scheme is implemented with fourth-order spatial accuracy within a flexible multi-block, body-fitted, hexahedral grid framework. An important feature of the high-order adaptive approach is that it allows for anisotropic refinement, which can lead to large computational savings when anisotropic flow features such as isolated propagating fronts and/or waves, shocks, shear surfaces, and current sheets are present in the flow. This approach is designed to handle complex multi-block grid configurations, including cubed-sphere grids, where some grid blocks may have degenerate edges or corners characterized by missing neighboring blocks. A procedure for building valid high-order reconstruction stencils, even at these degenerate block edges and corners, is proposed, taking into account anisotropic resolution changes in a systematic and general way. Furthermore, a non-uniform or heterogeneous block structure is used where the ghost cells of a block containing the solution content of neighboring blocks are stored directly at the resolution of the neighbors. A generalized Lagrange multiplier divergence correction technique is applied to achieve numerically divergence-free magnetic fields while preserving high-order accuracy on the anisotropic AMR grids. Parallel implementation and local grid adaptivity are achieved by using a hierarchical block-based domain partitioning strategy in which the connectivity and refinement history of grid blocks are tracked using a flexible binary tree data structure. Physics-based refinement criteria as well as the CENO smoothness indicator are both 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 approach.
Vorheriger Artikel A Fixed Mesh Method with Immersed Finite Elements for Solving Interface Inverse Problems
Nächster Artikel Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation

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Metadaten
Titel
High-Order Finite-Volume Method with Block-Based AMR for Magnetohydrodynamics Flows
verfasst von
L. Freret
L. Ivan
H. De Sterck
C. P. T. Groth
Publikationsdatum
12.10.2018
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 1/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0844-1

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