XFEM coupling techniques for landslide-fluid interaction

Selected topographies on earth are threatened by sudden landslides on natural or artificial hillsides. Dur- ing landslides natural granular materials exhibit phase transitions from solid-like to fluid-like behavior [1]. In order to describe such materials interacting with surrounding fluids a material formulation allow- ing a switch from solid- to fluid-like state is developed. The solid-like state of the granular is modeled as compressible elastic material in an eulerian framework, while the surrounding fluid is described by an incompressible newtonian fluid. Discretization of the balance equations is carried out with a stabilized space-time finite element method [2]. The domain of elastic material utilizes mixed-hybrid space-time elements while for the surrounding fluid standard velocity-pressure elements [3] are used. Interaction of both continua is described with an interface-coupled formulation where the level-set technique [4] is employed for the interface motion. The challenge of the introduced model is the coupling of fields with discontinuous state variables as well as fieldwise different state variables. Available coupling techniques in the context of the extended finite element method and based on localized mixed hybrid formulations [5] will be discussed and evaluated numerically by means of selected 2D examples.