A QUADRATIC PETROV-GALERKIN SOLUTION FOR KINEMATIC WAVE OVERLAND-FLOW

A Petrov-Galerkin (PG) finite element method was developed to solve th e kinematic wave formulation of the overland flow equations. The resul tant model uses quadratic basis functions and test functions that are modified by polynomials of cubic and quartic order, yielding a formula tion that includes four PH parameters. The PG model was found to reduc e the mean sum of square error of the solution compared to a conventio nal Bubnov-Galerkin finite element solution by about a factor of 3 as the Courant number (Cr) approached one. Good results were also achieve d with the PG method for problems that resulted in shock formation, wh ich are typical of many applied problems of concern. PG parameters wer e found to depend strongly upon the Courant number and weakly upon the number of nodes in the system. Polynomial expressions were derived to approximate the PG parameters over the range 0 < Cr < 1. As the numbe r of nodes in the system increased, a single-parameter version of the model yielded solutions approaching the accuracy of the four-parameter model.