Reliability Assessment of Computational River Models

Abstract

Application of numerical flood models in hydraulic engineering, loss and risk analysis, and urban policy making has increased significantly in recent years. While those models are widely being used, verification of underlying solvers and quality control (QC) of flood inundation results are still scarce among the hydraulic engineering community. This paper provides comprehensive verification methods/tools to fill this gap of knowledge. In this paper, the implementation of different code/solution verification procedures to build confidence in flood models was presented. The model verification approaches covered in this study includes: method of exact solution (MES), method of manufactured solution (MMS), Richardson extrapolation (RE), and the grid convergence index (GCI). Three test cases (steady subcritical flow, smooth transcritical flow, and dam-break shock formation) were used during the analyses to uncover all possible error/limitations in a shallow-water-wave solver. The asymptotic regime of convergence was used to select appropriate discretization sizes. The results from the MES and MMS indicate matched values for the observed and formal order of accuracy. For most of the discretization sizes, the observed order of accuracy indicates better performance for the water depth values than for the velocities. Although formal order of convergence is not achieved in some cases, the solution verification results show acceptable convergence behavior in the error norms as the grid resolution is refined. The RE and the GCI were successfully implemented for generating reference solutions and estimating the numerical uncertainty upper and lower bounds. Overall, this study provides a complete framework with essential set of tests to fully build a confidence in a flood model (1D or 2D) before applying it to solve real-world problems.