Accurate numerical simulation of landslides and dry granular avalanches plays a critical role in understanding geophysical hazards and informing risk mitigation strategies. This work presents a high-order numerical framework for modeling such flows based on depth-averaged Shallow Water Equations (SWE) extended by the Voellmy-Salm friction model, which combines Coulomb-type basal resistance and velocity-dependent turbulent drag. The Arbitrary Derivative Discontinuous Galerkin (ADER-DG) method, implemented within the ExaHyPE 2 simulation engine, enables unified high-order discretization in space and time, while explicitly resolving stiff source terms and non-conservative topographic interactions.

Stability near steep gradients and transient wet-dry interfaces is ensured through a modified CFL criterion and an a-posteriori sub-cell Finite Volume limiter.
In this approach, regions exhibiting non-smooth behavior are locally projected onto a first-order Finite Volume scheme using interface-based source treatment. Threshold-based limiting prevents nonphysical states, with hDry=0.001 m for synthetic slopes and hDry=0.1 m for realistic terrain.

The solver is validated on two representative scenarios. A benchmark case on a 35° inclined slope isolates the roles of frictional components, demonstrating physically consistent flow arrest under Coulomb friction and dissipative behavior under turbulent drag. A second test involving high-resolution digital elevation data from Norway's Tafjord region confirms the framework's robustness on complex topographies. Convergence studies indicate that sixth-order ADER-DG offers an optimal trade-off between accuracy and computational cost.

The results highlight the importance of tightly coupled numerical and physical modeling in granular flow simulations.  Future extensions may focus on improved interface fluxes beyond the Rusanov scheme, advanced wetting-drying treatments, adaptive DMP criterion, and multiphase extensions to simulate landslide-generated tsunamis.