期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 79, 期 1, 页码 176-208出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-018-0844-1
关键词
High-order finite volume scheme; Anisotropic block-based adaptive mesh refinement; Ideal magnetohydrodynamics (MHD) flows
资金
- Canadian Space Agency
- Natural Sciences and Engineering Research Council (NSERC) of Canada
- Canadian Space Agency through the Geospace Observatory Canada program
- Canada Foundation for Innovation (CFI)
- Province of Ontario, Canada
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.
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