Two-phase free-surface fluid dynamics on moving domains

We develop in this paper a model for the numerical simulation of free surface debris- and mudflows, described as a mixture of two viscous phases. A Lagrangian approach with finite element approximation and regular remeshing is adopted in this paper. The proposed model solves the equations of motion in both phases, coupled with conservation of volume of the mixture, implicitly; volume fractions are computed explicitly at the end of each iteration. A one-step trapezoidal scheme is used for time integration. The resulting model combines simplicity, robustness and versatility and provides a novel and unified algorithmic framework for a large spectrum of applications. It is also easily extensible to three spatial dimensions, more complex constitutive models and coupling with geomechanical models. Application to sedimentation and to impact on an obstacle shows the effectiveness of the approach.