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Dual reciprocity boundary element methods for water infiltration problems in irrigation
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Type
Thesis
Author
Imam Solekhudin
Supervisor
Ang, Keng Cheng
Abstract
Dual Reciprocity Boundary Element Methods (DRBEM's) are applied to solve problems involving infiltration from periodic irrigation channels into unsaturated homogeneous soils. The infiltration problems are governed by the Richards equation. These governing equations are then transformed into Helmholtz or modified Helmholtz equations before the methods are applied.
Four sets of problems are considered. The first set consists of problems involving steady in infiltration into homogeneous soils, in which the DRBEM is applied to solve the in infiltration problem from channels with negligible depth or at channels. Although fairly simple, this problem serves to demonstrate as well as evaluate the accuracy of the method. Numerical results obtained are then compared with published analytical solutions. In addition, the method is applied to solve problems of in infiltration from channels with three different cross-sectional shapes. The aim is to observe how the cross-sectional geometry affects the distribution of the Matric Flux Potential (MFP). We then consider in infiltration in three different types of homogeneous soil. The suction potential in the different soil types is compared.
The second set of problems improves on the first by incorporating root-water uptake into the problems. The governing equation is transformed into a modified Helmholtz equation, which is then solved using the DRBEM and a predictor-corrector scheme simultaneously. Numerical results obtained are compared with those from the corresponding problems without root-water uptake to study the effect of the root-water uptake on the MFP. The effect of the cross-sectional geometry of the channels is also examined. We then investigate in infiltration problems in different types of homogeneous soils. Effects of the soil type on the suction potential as well as the amount of water absorbed from the soil are investigated.
The third set of problems considers time-dependent in infiltration from periodic trapezoidal channels without root-water uptake. The governing equation is transformed into a Helmholtz equation as before. In this case, a Laplace transform is also used. The Stehfest formula is used to find the inverse Laplace transform numerically. From the MFP obtained, changes in the MFP distribution over the domain are studied.
The last set of problems involves time-dependent in infiltration with root-water uptake. The modified Helmholtz equation is solved numerically by applying the DRBEM and the predictor-corrector scheme simultaneously. Results are obtained, in terms of the MFP, and compared with those from the corresponding problem without root-water uptake to examine the effect of root-water uptake on the MFP.
We also study the change of the MFP with time.
Through the use of the DRBEM, this study has provided several useful and insightful results. The results seem to suggest that the cross-sectional geometry of the channel does not significantly affect water content in the soil. However, water content in the soil can be greatly in influenced by water absorption by the crops. For time-dependent problems, there is a time after which the increase in water content at a fixed level of soil remains constant. In addition, water content at a shallow level of soil reaches steady state values more rapidly than at deeper levels.
Four sets of problems are considered. The first set consists of problems involving steady in infiltration into homogeneous soils, in which the DRBEM is applied to solve the in infiltration problem from channels with negligible depth or at channels. Although fairly simple, this problem serves to demonstrate as well as evaluate the accuracy of the method. Numerical results obtained are then compared with published analytical solutions. In addition, the method is applied to solve problems of in infiltration from channels with three different cross-sectional shapes. The aim is to observe how the cross-sectional geometry affects the distribution of the Matric Flux Potential (MFP). We then consider in infiltration in three different types of homogeneous soil. The suction potential in the different soil types is compared.
The second set of problems improves on the first by incorporating root-water uptake into the problems. The governing equation is transformed into a modified Helmholtz equation, which is then solved using the DRBEM and a predictor-corrector scheme simultaneously. Numerical results obtained are compared with those from the corresponding problems without root-water uptake to study the effect of the root-water uptake on the MFP. The effect of the cross-sectional geometry of the channels is also examined. We then investigate in infiltration problems in different types of homogeneous soils. Effects of the soil type on the suction potential as well as the amount of water absorbed from the soil are investigated.
The third set of problems considers time-dependent in infiltration from periodic trapezoidal channels without root-water uptake. The governing equation is transformed into a Helmholtz equation as before. In this case, a Laplace transform is also used. The Stehfest formula is used to find the inverse Laplace transform numerically. From the MFP obtained, changes in the MFP distribution over the domain are studied.
The last set of problems involves time-dependent in infiltration with root-water uptake. The modified Helmholtz equation is solved numerically by applying the DRBEM and the predictor-corrector scheme simultaneously. Results are obtained, in terms of the MFP, and compared with those from the corresponding problem without root-water uptake to examine the effect of root-water uptake on the MFP.
We also study the change of the MFP with time.
Through the use of the DRBEM, this study has provided several useful and insightful results. The results seem to suggest that the cross-sectional geometry of the channel does not significantly affect water content in the soil. However, water content in the soil can be greatly in influenced by water absorption by the crops. For time-dependent problems, there is a time after which the increase in water content at a fixed level of soil remains constant. In addition, water content at a shallow level of soil reaches steady state values more rapidly than at deeper levels.
Date Issued
2013
Call Number
TA347.B69 Ima
Date Submitted
2013