Abstract
AbstractWhen the two‐dimensional shallow water equations are applied to solve practical irrigation problems, additional numerical difficulties arise. Large friction coefficients, dry bed conditions and singular infiltration terms engender new challenges which are addressed here to build a finite element method that is robust enough for this type of application. The proposed method is a stabilized formulation based on the symmetric quasi‐linear form and the set of entropy variables. The robustness of the method is increased with a discontinuity capturing operator. A predictor multi‐corrector algorithm is employed to solve the generalized trapezoidal rule. One of the novel features of the present technique is that an ‘explicit’ method has been developed with characteristics of implicit methods, so that the solution can be advanced at a convective CFL number of 1, regardless of the source terms. This leads to an economic procedure. Finally, an entropy production (in) equality is developed, which ensures the correct physical behaviour of the model and helps to determine the correct sign of the infiltration term. Copyright © 2002 John Wiley & Sons, Ltd.
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