Well-posed and stable boundary conditions for bedload transport equation (the 2D Exner Equation)

Sediment transport is a common process in environmental surface flows such as rivers, coasts or estuaries. The sediment particles can be transported by two basic mechanisms: suspended load that consists of the particles moving in the water column with the same velocity as the fluid, and bedload transport which accounts for the sediment mass moving by rolling and saltation mechanisms in a relatively thin layer over the static erodible stratum.

 

The bedload transport system of equations is composed of the two-dimensional shallow water equations for the free surface flow motion coupled to the 2D Exner or bedload transport equation for the erodible bed layer. The coupling to the bedload transport equation introduces an additional characteristic wave mode and complicated the derivation of well-posed and energy-stable boundary conditions.

 

The goal of this project is to derive and analysed well-posed and stable boundary conditions for the bedload transport equation. This is a necessary step towards the development accurate and robust numerical methods for modelling sediment transport problems in different applications.

Further comments: Programming in Python/MATLAB may be required. No previous knowledge of SBP operators is required.