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.

这项工作涉及使用混合稳定有限元在牛顿和粘塑性宾汉姆在自由表面流动时溢漏和泥石流的数值模型。主要目的是确定流体自由表面的位置。使用混合的稳定速度/压力有限元公式，正交子网格规模稳定（OSS）和拆分正交子网格规模稳定（Split-OSS）技术可实现速度和压力的等阶插值。引入双黏度正则化宾厄姆模型作为正则化Papanastasiou模型的替代方案。已经获得了泊瓦雪流的解析解，并进行了收敛测试以比较两个模型。提出了一种在固定网格上求解的简化欧拉方法，以跟踪自由表面的运动。通过使用稳定的水准仪固定方法运输自由表面来完成此操作。将数值解与文献中的分析，实验结果和数值基准进行了比较。在实际案例研究中，还将它们与现场数据进行了比较，这些数据是由于采矿储层故障而产生的流量，并通过3D和2D简化模型进行了求解。