Performance comparison of overland flow algorithms

Two regional models, the South Florida Water Management Model (SFWMM) and the Natural System Model (NSM), are applied to analyze and predict water conditions in the Everglades and South Florida. Both of these models use an alternating direction explicit (ADE) type method to solve diffusion flow. In this paper, three finite-difference algorithms based on explicit, alternating direction implicit (ADI) and successive over relaxation (SOR) methods are examined as possible replacements for the ADE method. Various model solutions are verified using an axisymmetric test problem that is solved using an axisymmetric test model. A comparison of run time versus error plots proved that the ADI method has the best overall performance. The study includes a description of the relationship between the accuracies and run times of different algorithms and their spatial and temporal discretizations in dimensionless form. Linear and spectral analyses are used to derive theoretical expressions for numerical error, run time, and stability, Comparisons indicate that theoretical estimates of numerical error and run times closely approximate the experimental values. Results of this study are valuable as methods to determine optimum space and time discretizations of future modeling applications when the maximum allowable numerical error and the dimensions of the flow features to be simulated are known. Results can also he used to understand the magnitudes of numerical errors in existing modeling applications.