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Efficient simulation of single species and multispecies transport in groundwater with local adaptive grid refinement
Author(s) -
Wolfsberg Andrew V.,
Freyberg David L.
Publication year - 1994
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/93wr02749
Subject(s) - grid , computer science , modular design , computational science , algorithm , a priori and a posteriori , partial differential equation , sharpening , mathematical optimization , mathematics , geometry , artificial intelligence , mathematical analysis , philosophy , epistemology , operating system
The computational burden associated with multidimensional, multicomponent, numerical solute transport models can be prohibitive. To solve these CPU intensive problems efficiently and accurately, we have implemented and extended a local adaptive grid refinement method of Berger and Oliger (1984) to track error‐prone regions and supply high‐resolution subgrids where they are locally needed while maintaining relatively few nodes elsewhere on a coarse, base grid. Novel features include a unique method for detecting a priori where the numerical error is unacceptable, variable time step control which allows smaller time steps on subgrids than on the base grid, and a modular framework which allows easy exchange of partial differential equation solvers to accommodate different problem formulations. Three examples show how the subgrids track the error‐prone regions, how multiple subgrids are used for geometrically complex front shapes, and how increased resolution is provided for self‐sharpening fronts when multiple reacting species are considered. For all three examples, solutions with accuracies comparable to those achieved with a uniform fine grid are obtained at between 20 and 30% of the computational cost.