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United States Department of Agriculture

Agricultural Research Service

Title: Accuracy of Numerical Methods for Solving the Advection-Diffusion Equation As Applied Tospore and Insect Dispersal

Authors
item Yang, Y - TEXAS A&M UNIV
item Wilson, L - TEXAS A&M UNIV
item Makela, M - TEXAS A&M UNIV
item Marchetti, Marco

Submitted to: Ecological Modeling
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: December 1, 1997
Publication Date: N/A

Interpretive Summary: In order to increase the accuracy of a model for predicting describing the development and spread of plant disease or insect infestation in field crops, it is necessary to include equations to account for the dispersal of disease-causing spores and insects by air. This paper demonstrates and discusses which of several numerical methods best describes their dispersal lfor the purpose of predicting the spread of disease in the field.

Technical Abstract: Three algorithms for solving a simplified 3-D advection-diffusion equation were compared as to their accuracy and speed in the context of insect and spore dispersal. The algorithms tested were the explicit central difference (ECD) method, the implicit Crank-Nicholson (ICN) method, and the implicit Chapeau function (ICF) method. The three algorithms were used only to simulate the diffusion process. A hold-release wind shifting method was developed to simulate the wind advection process, which shifts the concentration an integer number of grids and accumulates the remaining wind travel distance (which is less than the grid spacing) to the next time step. The test problem was the dispersal of a cloud of particles (originally in only one grid cell) in a 3-D space. The major criterion for testing the accuracy was R-squared, which represents the proportion of the total variation in particle distribution in all grid cells that is accounted for by the particle distribution through numerical solutions. High R-squared values were obtained for the ECD method and for the two implicit methods. The ICN method gave higher R-squared values than the ICF method when the concentration gradients were high, but its accuracy decreased more rapidly with the progress of time than the ICF method. Based on the R-squared value and the requirement for concentration positivity, for simulations with steep concentration gradients, the ECD method would be most appropriate, followed by the ICN method. For simulations with low concentration gradients, the ECD, ICF, or ICN method could be used, but the ICN method would not be appropriate with a large step and a large grid spacing.

Last Modified: 7/23/2014
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