Numerical Modelling of Viscoplastic Free Surface Flows in Complex 3d Geometries

We study a numerical method for the simulation of free surface flows of viscoplastic (Herschel-Bulkley) fluids. The approach is based on the level set method for capturing the free surface evolution and on locally refined and dynamically adapted octree cartesian staggered grids for the discretization of fluid and level set equations. We consider an extension of the stable approximation of the Newtonian flow equations on staggered grid to approximate the visoplastic model and level-set equations if the free boundary evolves and the mesh is dynamically refined or coarsened. In the Newtonian case, the convergence of numerical solutions is observed towards experimental data when the mesh is refined. We compute several viscoplastic Herschel-Bulkley fluid flows over incline planes for the dam-break problem. The comparison of numerical solutions is done versus experimental studies, indicating that intrinsically 3D numerical simulations are often required to compare well with a physical experiment. The efficacy of the numerical approach is demonstrated for a real-life application of landslide runout modelling in the Western Sayan mountains. Kirill D. Nikitin, Maxim A. Olshanskii, Kirill M. Terekhov and Yuri V. Vassilevski