Numerical Methods 101  Convergence of Numerical Models
 Publication Year:
 1992

 Bepress 7450

 Bepress 98
article description
A numerical model is convergent if and only if a sequence of model solutions with increasingly refined solution domains approaches a fixed value. Furthermore, a numerical model is consistent only if this sequence converges to the solution of the continuous equations which govern the physical phenomenon being modeled. Given that a model is consistent, it is insufficient to apply it to a problem without testing for sensitivity to the size of the time and distance steps which form the discrete approximation of the solution domain. That is, convergence testing is a required component of any modeling study. Two models were examined for this paper. The first model is a fourpoint implicit method applied to the unsteady onedimensional openchannel flow equations. The second model is an unsteady onedimensional or depthaveraged twodimensional explicit diffusionwave approximation of the shallowwater flow equations. Both models were applied to a onedimensional channel problem. The twodimensional model was applied to a simple twodimensional flow field. Convergence testing is demonstrated in this paper by applying these models and examining the impact of increased spatial and temporal resolution on the results. It is demonstrated that both models are sensitive to changes in the spatial resolution and that erroneous solutions may result if this sensitivity is not understood during application of these models.