Numerical Analysis and Scientific Computing Preprint Seria A unified approach for computing tsunami, waves, floods, and landslides

The prediction of large-scale hydrodynamic events such as tsunami spread and run-up, dam break, flood, or landslide run-out is a challenging and important problem of applied mathematics and scientific computing. The paper presents a computational approach based on free surface flow models for fluids of complex rheology to simulate such events and phenomena with detail and prediction confidence typically not achievable by simplified models. Using nonlinear defining relations for stress and rate of strain tensors allows a unified approach to simulate events described by both the Newtonian model (tsunami, dam break) and non-Newtonian models (landslide, snow avalanches, lava flood, mud flow). The computational efficiency of the numerical approach owes to the level-set method for free surface capturing and to an accurate and stable FV/FD method on dynamically adapted octree meshes for discretization of flow and level set equations. In this paper we briefly describe the numerical method and present results of several simulations of hydrodynamic events: a dam break, a landslide and tsunami spread and run-up.