Landslides are natural disasters that can have serious consequences for the surrounding areas, including the humans living there. Thus, it is paramount to better understand their physics and integrate this theoretical knowledge into numerical simulations. 

This thesis starts by concisely summarizing the relevant governing equations in the form of the 2D Shallow water equations. In the case of landslides, this thesis expands these basic equations by incorporating a friction term. 
Further attention is then paid to approximate methods to solve these equations. Therefore, both the Finite Volume method as well as the Riemann Problem are introduced.

After this theoretical summary, the thesis starts evaluating different numerical methods, namely different approximate Riemann Solvers. The simple but robust Rusanov Solver, the more sophisticated HLLC Solver, and the more complicated Augmented Riemann Solver are investigated. Common problems with these solvers, e.g., Wetting and Drying mechanisms and well-balancedness, are discussed, as well as numerical solutions to robustly handle them. 

After these numerical aspects are evaluated, 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 experimental results or be evaluated based on physical feasibility.