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The Courant and Peclet Number criteria for the numerical solution of the Richards Equation
Author(s) -
ElKadi Aly I.,
Ling Ge
Publication year - 1993
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 - 10.1029/93wr00929
Subject(s) - mathematics , convergence (economics) , péclet number , conservation of mass , numerical analysis , mathematical optimization , rate of convergence , computer science , mathematical analysis , mechanics , physics , computer network , channel (broadcasting) , economics , economic growth
Recent studies indicate that inaccuracies exist in the numerical solutions of the Richards equation. A need exists to examine such inaccuracies and to correlate them, formally, to the soil hydraulic properties and the size of the spatial and temporal mesh. In the absence of criteria for mesh design, mass conservation and the rate of convergence are usually used as bases for acceptance of the solution. It is well documented, however, that neither can guarantee an accurate solution. This paper proposes the Courant and Peclet numbers as criteria for estimating spatial and temporal increments. The study defines upper limits of these numbers for acceptable accuracy of the numerical solutions. For cases that are characterized by decreasing pressure head gradients, although the initial size of the time step may be extremely small, efficient solutions are possible through a careful choice of an expansion factor for such a step.