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Numerical error in groundwater flow and solute transport simulation
Author(s) -
Woods Juliette A.,
Teubner Michael D.,
Simmons Craig T.,
Narayan Kumar A.
Publication year - 2003
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 - 10.1029/2001wr000586
Subject(s) - computer simulation , benchmark (surveying) , numerical analysis , numerical stability , gaussian , stability (learning theory) , mathematics , flow (mathematics) , dispersion (optics) , code (set theory) , computer science , groundwater flow , finite element method , mechanics , groundwater , simulation , geotechnical engineering , geology , engineering , physics , structural engineering , mathematical analysis , machine learning , programming language , optics , geodesy , quantum mechanics , aquifer , set (abstract data type)
Models of groundwater flow and solute transport may be affected by numerical error, leading to quantitative and qualitative changes in behavior. In this paper we compare and combine three methods of assessing the extent of numerical error: grid refinement, mathematical analysis, and benchmark test problems. In particular, we assess the popular solute transport code SUTRA [ Voss , 1984] as being a typical finite element code. Our numerical analysis suggests that SUTRA incorporates a numerical dispersion error and that its mass‐lumped numerical scheme increases the numerical error. This is confirmed using a Gaussian test problem. A modified SUTRA code, in which the numerical dispersion is calculated and subtracted, produces better results. The much more challenging Elder problem [ Elder , 1967; Voss and Souza , 1987] is then considered. Calculation of its numerical dispersion coefficients and numerical stability show that the Elder problem is prone to error. We confirm that Elder problem results are extremely sensitive to the simulation method used.