Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 pp 343-355 | Cite as

# A Parallel High-Order CENO Finite-Volume Scheme with AMR for Three-Dimensional Ideal MHD Flows

## Abstract

A highly-scalable and efficient parallel high-order finite-volume method with local solution-dependent adaptive mesh refinement (AMR) is described for the solution of steady plasma flows governed by the equations of ideal magnetohydrodyamics (MHD) on three-dimensional multi-block body-fitted hexahedral meshes, including cubed-sphere grids based on cubic-gnomonic projections. The approach combines a family of robust and accurate high-order central essentially non-oscillatory (CENO) spatial discretization schemes with a block-based anisotropic AMR scheme. The CENO scheme is a hybrid approach that avoids some of the complexities associated with essentially non-oscillatory (ENO) and weighted ENO schemes and is therefore well suited for application to meshes having irregular and unstructured topologies. The anisotropic AMR method uses a binary tree and hierarchical data structure to permit local refinement of the grid in preferred directions as directed by appropriately selected refinement criteria. Applications will be discussed for several steady MHD problems and the computational performance of the proposed high-order method for the efficient and accurate simulation of a range of plasma flows is demonstrated.

## Notes

### Acknowledgements

This work was supported by the Canadian Space Agency and by the Natural Sciences and Engineering Research Council (NSERC) of Canada. In particular, the authors would like to acknowledge the financial support received from the Canadian Space Agency through the Geospace Observatory Canada program. Computational resources for performing all of the calculations reported herein were provided by the SciNet High Performance Computing Consortium at the University of Toronto and Compute/Calcul Canada through funding from the Canada Foundation for Innovation (CFI) and the Province of Ontario, Canada.

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