Premium
Numerical stability and accuracy of implicit integration of free surface groundwater equations
Author(s) -
Liu Philip L.F.,
Liggett James A.
Publication year - 1980
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/wr016i005p00897
Subject(s) - weighting , stability (learning theory) , mathematics , time derivative , mathematical analysis , free surface , boundary value problem , numerical stability , surface (topology) , finite difference , zero (linguistics) , numerical analysis , mechanics , physics , geometry , computer science , machine learning , linguistics , philosophy , acoustics
In the solution of two‐ or three‐dimensional free surface flow the time‐dependent boundary condition is represented in an implicit finite difference form. The numerical solution may damp or amplify the real solution or contain oscillations, either stable or unstable, about the real solution, depending on the weighting factor θ (which positions the space derivative in time) and the wave number of the solution mode. Zero numerical damping occurs at a value of 0.5 < θ < 0.6; the exact value of θ depends on the wave number and length of the time step. The paper provides a guide for choosing θ and the time step.