Shallow Water Flows Including Sediment Transport and Morphodynamics

The purpose of this project is to understand the tranport and deposit of sediment caused by flowing water, particularly in rivers or lakes.

To accomplish this, the project aims to mathematically model and numerically simulate the propagation of said water waves and their influence on sediment displacement.

The evolution of the water waves as well as the morphology of the sediment layer are modelled by partial differential equations. Due to the complexity and coupling of thsee underlying models, analytical solutions do not exist.

Thus, the core of this project is to design novel and robust numerical methods that approximate such wave propagation and sediment transport. The backbone of these numerical schemes is a high-order discontinuous Galerkin spectral element method. Stability is first investigated on the continuous level with the creation of energy estimates.

This stability estimate is transferred onto the discrete level through the use of special discrete derivative operators.

Beyond provable stability, the numerics developed in this project will also ensure that the approximate solution remains physically relevant.

In doing so, the approximate solutions generated by the numerics remain compatible to the real-world evolution of water tables as well as comparable to available observation data.

Also, practical considerations will be made in the project to implement the novel algorithms on modern parallel computing frameworks and release them as open source software.