溃坝水流数值计算的非结构有限体积模型

Unstructured finite volume model for numerical simulation of dam-break flow

针对溃坝洪水数值计算面临不规则边界和复杂地形等问题,建立了三角形网格下求解二维浅水方程的高精度Godunov型有限体积模型。空间上,引入变量重构和限制器技术,采用HLLC近似Riemann算子计算数值通量;时间上,采用Hancock预测-校正法。将底高程定义于单元顶点,结合单元水位～体积关系,提高了干湿界面处理能力。采用单元中心型底坡项近似,并通过构造通量修正项,保证了格式的和谐性。分析并采用改进的半隐式格式解决了摩阻项可能引起的刚性问题。算例研究结果表明,模型稳定,和谐性好,具有较好的推广应用价值。

A high-performance Godunov-type finite volume scheme is proposed for numerical simulation of dam-break flow over highly irregular terrain with complex geometries.The scheme is used to solve the two-dimensional shallow water equations on triangular grids.Using the variable reconstruction and limiter techniques,the numerical flux can be calculated with the HLLC（Harten-Lax-van Leer-Contact） solver.The Hancock predictor-corrector method is adopted for time stepping.The bed elevation is assigned to the vertices of grids,which is beneficial to wet/dry fronts treatments.The flux correction terms combined with the central approximation for the central bed slope source term can preserve a well-balanced property.The stiff problem due to the friction term is investigated,and a semi-implicit scheme is proposed to treat the issue.Numerical results from test examples show that the new scheme is stable,robust,and well-balanced,thus having a wide range of application prospects.