Modeling of spillage and debris floods as Newtonian and viscoplastic Bingham flows with free surface with mixed stabilized finite elements

Abstract

• Numerical modelling of Newtonian and viscoplastic Bingham flows with free surface. • Study of flow due to dam-break resulting in spillage and debris floods. • Mixed velocity/pressure element with Orthogonal Subgrid Scale stabilization. • Accurate determination of the location of the free surface of the flow. • Analytical solution to a Poiseuille flow. This work deals with the numerical modeling of spillage and debris floods as Newtonian and viscoplastic Bingham flows with free surface using mixed stabilized finite elements. The main objective is the determination of the location of the free surface of the flow. A mixed stabilized velocity/pressure finite element formulation is used and the Orthogonal Subgrid Scale stabilization (OSS) and the Split Orthogonal Subgrid Scale stabilization (Split-OSS) techniques enable equal order interpolation for velocity and pressure. A double viscosity regularized Bingham model is introduced as an alternative to the regularized Papanastasiou model. The analytical solution to a Poiseuille flow has been obtained and a convergence test has been performed to compare both models. A simplified Eulerian method solved on a fixed mesh is presented to track the movement of the free surface. This is done by transporting the free surface with a stabilized level set method. The numerical solutions are compared with analytical, experimental results and numerical benchmarks from the literature. They are also compared with field data in a real case study, the flow due to the failure of a mining reservoir, which is solved in 3D and as a 2D simplified model.