Efficient two-dimensional simulation models for hydraulic and morphodynamic transients

Pilar García-Navarro

One-dimensional (1D) models have traditionally been used for hydraulic and morphodynamics prediction in large river reaches, mainly because they run fast due to the simplified flow equations used. However, in complex floodplains or where the flow is unconfined, 1D models may not provide an adequate solution due to the limitations of uniform water velocity and constant water surface elevation on each cross section. This warrants the use of more accurate two-dimensional (2D) models. However, the numerical solution of the 2D hydrodynamic equations and the requirement of flexible meshes had made 2D models considerably more demanding in computer times than 1D models. This drawback becomes even more when constraining when including bed processes in the system. Recent advances in the simulation of free surface flows over mobile bed have shown that accurate and stable results in realistic problems can be provided if a coupling between the shallow water equations (SWE) and the Exner equation is performed. Different approaches have been proposed leading to a variety of models with different complexity and computational cost. Therefore, for restoring the numerical efficiency, the coupling technique is simplified, not decreasing the number of waves involved in the Riemann problem but simplifying their definitions. The simplified model is formulated under a general framework able to insert any desirable discharge solid load formula. As a result, faithful numerical predictions are available for a wide range of flow conditions and empirical bed load discharge formulations, allowing the investigation of the best option in each case study, which is mandatory in these type of environmental problems. The effects of the approximations made are tested against experimental data which include transient problems over erodible bed. Furthermore, recent advances in massive parallelization techniques for 2D hydraulic models are able to reduce computer times by orders of magnitude making 2D applications competitive and practical for operational flood prediction in large river reaches. Moreover, high performance code development can take advantage of general purpose and inexpensive Graphical Processing Units (GPU), allowing to run 2D simulations more than 100 times faster than old generation 2D codes, in some cases.