Comparative Analysis of Laplace Transform and Finite Difference Modeling and Simulation of Solute Transport in Soil. (Case Study: Nitrate Solute Transport in Homogeneous Soil)
Analytical Laplace transform and numerical finite difference methods were used to solve solute transport model (conversion dispersion equation) for a simplified homogeneous soil and simulation of the transport were done using Matlab programming language. Nitrate solute was used for the study. The study compared the simulation results that were generated by both the Laplace transform and the finite difference methods. Spatial and Temporal simulation of nitrate transport comparing both analytical and numerical solutions were presented. The errors in the spatial and temporal numerical solution were simulated. A three dimensional simulation of the nitrate concentration, depth and time for both the Laplace transform and the finite difference method were also presented. The results showed that finite difference numerical method gave a good approximation of the Laplace transform analytical method which provide exact solution. Although there were errors associated with the numerical solution, the output of the numerical solution do not sharply deviate from that of the analytical solution. The errors associated with the finite difference numerical solution were mainly as a result of truncation of the Taylor series expression.
Finite difference numerical method can be used to model solute transport in heterogeneous soil which is a more complex process that cannot be accomplished with analytical method with a reasonable level of accuracy. Modeling of solute transport in soil is essential for management of nutrients supply to plants and water resource.
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