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
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摘要: 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。Abstract: A highperformance Godunovtype finite volume scheme is proposed for numerical simulation of dambreak flow over highly irregular terrain with complex geometries.The scheme is used to solve the twodimensional shallow water equations on triangular grids.Using the variable reconstruction and limiter techniques,the numerical flux can be calculated with the HLLC (HartenLaxvan LeerContact) solver.The Hancock predictorcorrector 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 wellbalanced property.The stiff problem due to the friction term is investigated,and a semiimplicit scheme is proposed to treat the issue.Numerical results from test examples show that the new scheme is stable,robust,and wellbalanced,thus having a wide range of application prospects.