Weighted Implicit Finite-Volume Model for Overland Flow

A weighted implicit finite-volume model is developed to simulate two-dimensional diffusion flow in arbitrarily shaped areas. The model uses a mixture of unstructured triangles and quadrilaterals to discretize the domain, and a mixture of cell wall types to describe structures, levees, and flow functions that characterize two-dimensional flow. The implicit formulation makes the model stable and run faster with very large time steps. The sparse system of linear equations that results from the implicit formulation is solved by using iterative solvers based on various preconditioned conjugate gradient methods. The model was tested under a variety of conditions. The results were compared with results from known models applied to axisymmetric and other test problems that had known solutions. The model was applied successfully to the Oxbow section of the Kissimmee River in Florida, and the results were compared with results from physical and numerical modeling studies. This analysis indicated that the circumcenter-based flow function for walls that is used in the model gives overall superior results in all the cases considered. Results of the numerical experiments showed that the use of weighted implicit methods and iterative solvers provide modelers with improved flexibility and control of the overall accuracy and the run time. The method is to be used as an efficient solution method for local and regional modeling problems in south Florida.