J. Jpn. Soc. Soil Phys.
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No. 22, p. +3,/ ,**+ῌ
 PDE    *
Application of a General PDE Solver for Analyzing
Water and Solute Transport in SoilKosuke NOBORIO** Faculty of Agriculture, Iwate University, Morioka *,*ῌ2//*, JapanAbstract
For the proper management of water and fertilizer resources, distributions of water and solutein soil should be precisely predicted.

The movement of water and solute in soil may be expressedwith partial di#erential equations (PDEs).

The PDEs should be numerically solved for real worldapplications because of complex initial and boundary conditions and high non-linearity in somecases.

The recent development of a general PDE solver using the ﬁnite element method enabled

us to more easily solve these PDEs governing water and solute transport in soil. FlexPDE Lite
can be freely obtained through the Internet, and its applicability to solve water and solutetransport in soil was investigated. FlexPDE Lite successfully simulated water inﬁltration into
Haverkamp’s sandy soil with ῍,῎ of mass balance errors.

However, it failed to calculate waterinﬁltration into dry loamy sand when initial pressure head was 0* cm.

Results of simulating

solute transport with FlexPDE Lite also agreed well with analytical solutions especially when theconvective transport was not dominant. Therefore, FlexPDE Lite, although its performanceswere purposely limited, could be an ideal tool for a training purpose or a smalloscale simulation.
Keywords : numerical solution, ﬁnite element method, soil water movement, solute transport,
simulation model+    

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and Vachaud, G. (+311) : A comparison of numerical simulation models for oneodimensional inﬁltration, Soil Sci. Soc. Am. J., .+ : ,2/ῌ,3..

* P/[L ;\]^ _ `; ab X" cHuyakorn, P.S. and Nilkuha, K. (+313) : Solution ofd  ef0 gh iX j ;klLtransient transport equation using an upstreamlj mnoﬁnite element scheme, Appl. Math. Modelling, - :FlexPDE Lite 6pqrstu vwWxyz{!" cd |}~f6;6=

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Javandel, I., Doughty, C. and Tsang, C.F. (+32.) :FlexPDE Lite !" >  .** <5Groundwater transport : Handbook of mathe-;uW ' ;L "  

matical models, Water Resour. Monogr. +*, AmJK^o !;" JK;5W;=;" s/B~Xῌ Geophys. Union, Washington, D.C.
Noborio, K., McInnes, K. J. and Heilman, J.L. (+330) : !HXJK6

Twoodimensional model for water, heat, andwW EF~X. A¡¢6£

solute transport in furrowoirrigated soil : I.

¤6]" ¥¦§¨©-D6BCq Theory, Soil Sci. Soc. Am. J., 0* : +**+ῌ+**3.

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Richards, L.A. (+3-+) : Capillary conduction of liquids!®6=¯°wW FlexPDE Lite !" http :through porous media, Physics, + : -+2ῌ---.

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25

unsaturated soils. Soil Sci. Soc. Am. J., .. : 23,ῌof soil analysis. Part +, ,nd ed. Agron. Monogr. 3,

232.

ASA and SSSA, Madison, WI.

van Genuchten, M.Th. and Wierenga, P. (+320) :Solute dispersion coe$cients and retardation
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