Accuracy of the Local Inertia Approximation solver and the importance of Large Eddy Simulation in 2D hydrodynamical models on steep-sloped watersheds

Hydrodynamical models on watersheds with high flash-flood risk are useful tools. Although it is important to know how reliable a model is for calculating aspects of the overland flow.

Steep-sloped, natural watersheds have sudden geometrical changes. The slope alteration on the overland flow area, the chaotic meandering of the natural stream beds cause complex turbulent flow.

In average, hydrodynamical models with solvers based on the full depth integrated Shallow Water Equations (SWE) can be accepted as the most accurate methods. On the other hand, the SWE based models can easily become unstable due to the changes in geometry. If a simulation becomes unstable, to increase stability simplifications can be necessary. The Local Inertia Approximation (LIA) is a simplified method, where nonlinear advection is neglected. Although with the simplification the proper representation of the turbulent flow can be lost.  Therefore, additional methods are required to regain the proper turbulent effect without the sacrifice of the model’s stability.

The Large Eddy Simulation (LES) can be a suitable additional part for the overland flow model. The method’s task is to increase the model’s accuracy on the calculation of the turbulent flow.

This research uses artificial watersheds to compare different modelling methods thru stable calculations. The goal is showing how simplified hydrodynamical models’ accuracy can be amplified on calculating turbulent overland flow.

Keywords: numerical modelling, hydrodynamics, shallow water equation, local inertia, overland flow, watershed model