带有障碍物溃坝流动问题的有限元数值模拟研究

针对下游带有障碍物的溃坝流动问题,本文基于两相流动模型,在有限元算法框架下对其进行数值模拟研究。依据水平集(Level Set)方法追踪运动界面,并引入了一个简单的修正技术,保证较好的质量守恒性。为了精确表示运动界面,采用稳定和有效的间断有限元方法求解双曲型Level Set及其重新初始化方程。对于两相统一Navier-Stokes方程,首先利用分裂格式对其解耦,然后通过SUPG (Streamline Upwind Petrov Galerkin)方法进行数值求解。模拟研究了下游带有障碍物的牛顿流体溃坝流动问题,得到的数值结果与文献已有模拟结果及实验结果均吻合较好。此外,还考虑了幂律型非牛顿流体,并分析了不同特性非牛顿流体对于溃坝流动过程和界面形态等的影响。

The finite element numerical investigation of dam-break flow with obstacle

In this paper,we study the dam-break flow with obstacles via the finite element computational framework.We simulate this problem based on a two-phase flow model.The Level Set method is used to capture the moving interface and a simple correction technique is introduced to guarantee the mass conservation property.The Level Set and its re-initialization equations are all hyperbolic equations.Thus,we solve them using the stable and efficient discontinuous Galerkin method.As for the unified Navier-Stokes equation,we first decouple it via splitting scheme,and then solve the sub-equations using Streamline Upwind Petrov-Galerkin method.We first simulate the Newtonian fluid (water) dam-break flow with obstacles in the downstream are.Our numerical results are all identical to other numerical and experimental results in the literature.In addition,we also consider the non-Newtonian fluids,which are described by the power-law model.The influences of different non-Newtonian fluids on the whole flow process and interface profiles are analyzed.