Divergence- and Curl-Preserving Prolongation and Restriction Formulas |
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Authors: | G. T th,P. L. Roe |
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Affiliation: | University of Michigan, Ann Arbor, Michigan, f1;University of Michigan, Ann Arbor, Michigan, , f2 |
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Abstract: | We present new second-order prolongation and restriction formulas which preserve the divergence and, in some cases, the curl of a discretized vector field. The formulas are suitable for adaptive and hierarchical mesh algorithms with a factor-of-2 linear resolution change. We examine both staggered and collocated discretizations for the vector field on two- and three-dimensional Cartesian grids. The new formulas can be used in combination with numerical schemes that require a divergence-free solution in some discrete sense, such as the constrained transport schemes of computational magnetohydrodynamics. We also obtain divergence-preserving interpolation functions which may be used for streamline or field line tracing. |
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Keywords: | Abbreviations: numerical approximationAbbreviations: magnetohydrodynamics |
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