Solution of the Transport Equation by the Collocation Method in Conjunction With the Adaptive Hermite Element Family

The solution of the advection‐dominated transport equation exhibits behavior whose structure is localized in small subregions of the spatial domain. This requires placing a high‐resolution spatial grid in their vicinity. In an attempt to increase the spatial resolution, a family of 16 adaptive Hermi...

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Bibliographic Details
Published in:Water resources research 1990-11, Vol.26 (11), p.2661-2677
Main Authors: Bhuiyan, Muhammed A., Allayla, Rashid I., Hussain, Tahir, Ishaq, Achi M., Mohsen, M. F. N.
Format: Article
Language:English
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Summary:The solution of the advection‐dominated transport equation exhibits behavior whose structure is localized in small subregions of the spatial domain. This requires placing a high‐resolution spatial grid in their vicinity. In an attempt to increase the spatial resolution, a family of 16 adaptive Hermite elements has been developed. Collocation methodology in conjunction with these adaptive families produces a matrix whose bandwidth is larger than using cubic Hermite elements all over the solution domain. A special technique is devised to condense out this bandwidth prior to the solution of the global system. The numerical solutions are tested against the available one‐ and two‐dimensional analytical solutions. For the discretization attempted, the code was tested up to a Peclet number of 600 in one dimension and 200 in two dimensions.
ISSN:0043-1397
1944-7973
DOI:10.1029/WR026i011p02661