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Mudflows are catastrophic events that cause immense damage to infrastructure and life every year. Measures to mitigate the risk are in most cases designed based on knowledge from past events. Numerical models have started emerging about 30 years ago. While a variety of depth-averaged models are available and implemented in commercial software almost no continuum models exist, that would allow the extraction of forces acting on buildings and protection structures. Moreover, no two-phase material models exist that allow the simulation of the complete process of initiation, propagation and stopping of a flow. The proposed two-phase model formulates the equations of free-surface flow of a two-phase mixture in a moving reference frame. The problem of updating the positions of the nodes of two phases is solved by re-creating a new mesh after each update. The nodal variables are mapped onto this new mesh by linear interpolation. The computation of volume fractions of the two phases is de-coupled from the computation of the main nodal variables. Test problems illustrate the versatility of the method for simulating a wide variety of problems of two-phase flow.