The topic of this thesis is landslide and water simulations with a focus on their numerical aspects. This thesis starts by concisely summarizing the relevant governing equations in the form of the basic two-dimensional shallow water equations. In the case of landslides, this thesis expands these basic equations by incorporating a Coloumb-type friction term. Thus, it treats landslides as dry one-layer granular flows. This work then pays further attention to approximate methods to solve these equations. Therefore, both the finite volume method and the Riemann problem are introduced. After this theoretical summary, the thesis starts evaluating different numerical methods, namely approximate Riemann solvers. This work investigates the simple but robust Rusanov solver, the more sophisticated HLLC Solver, and the more complicated augmented Riemann solver. Afterwards, the thesis considers common problems with these solvers, e.g., wetting and drying mechanisms and well-balancedness, and numerical solutions to handle them robustly. After evaluating these numerical aspects, this thesis will demonstrate their feasibility and correctness through a series of different numerical validation cases. These cases, as well as the respective solvers, are implemented in ExaHyPE 2. This implementation comprises both shallow-water and landslide scenarios. The numerical results will be compared to either the analytical solution or be evaluated based on physical feasibility. The outllok will describe further developments and experiments to improve the respective solvers and scenarios.     «

The topic of this thesis is landslide and water simulations with a focus on their numerical aspects. This thesis starts by concisely summarizing the relevant governing equations in the form of the basic two-dimensional shallow water equations. In the case of landslides, this thesis expands these basic equations by incorporating a Coloumb-type friction term. Thus, it treats landslides as dry one-layer granular flows. This work then pays further attention to approximate methods to solve these equa...     »