Janice Ayog

Research Project: Simplified Two-dimensional Second-order Discontinuous Galerkin Flood Model For Real-world Applications

Discontinuous Galerkin (DG) methods have emerged as a viable alternative to classical numerical schemes (i.e. finite difference, finite element and finite volume) found in many popular industrial two-dimensional (2D) flood modelling software packages.

DG methods essentially combine the locally-conservative finite volume principles and the flexibility of the finite element weak formulations.This feature made DG methods a natural high order extension to the finite volume methods while still retaining locality.

In achieving higher order accuracy however, the mathematical complexity constructed within the DG formulations have to be increased, eventually affecting their stability, robustness and efficiency (in runtime costs) in simulating real-world flooding scenarios.

Furthermore, the presence of irregular topography and structures with very steep gradients (commonly encountered in urban catchments) may also compromise the stability of the DG methods, thus requiring extensive pre-treatment of the terrain data prior to flood model setup.

These issues are largely why DG methods are not widely used in studies pertaining to flood risk management and are only at most second-order accurate.

My PhD research is to develop a DG flood model that is simple in its mathematical complexity, yet stable and robust for practical purposes of flood modelling.

To achieve this aim, three objectives have been formed: a) to formulate a DG numerical method that is simple and robust, and assess its performance and predictive capability over academic and experimental test cases; b) to benchmark the reformulated DG flood model against existing industrial and alternative research flood models and finally, to adapt the reformulated DG model for the simulation of real-world flooding scenarios.