Abstract
An orthogonal upstream weighting finite element scheme is presented for approximating the contaminant transport equation, that will result in a matrix amenable to the pointwise solution strategies. Orthogonal upstream weighting functions are derived for line, quadrilateral, and triangular elements. Numerical experiments indicate that the direct elimination solutions of the proposed scheme yield comparable results as those obtained by the Galerkin and non-orthogonal upstream schemes. When the successive over-relaxation is applied to solving the matrix equation, the former generates convergent solutions for all cases. In contrast, the latter result in convergent solutions only for dispersion dominant transport, but produce divergent computations for advection dominant transport.
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Yeh, G.T. (1984). Solution of Contaminant Transport Equations Using an Orthogonal Upstream Weighting Finite Element Scheme. In: Laible, J.P., Brebbia, C.A., Gray, W., Pinder, G. (eds) Finite Elements in Water Resources. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11744-6_24
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DOI: https://doi.org/10.1007/978-3-662-11744-6_24
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