摘要
构建了动态局部自适应网格系统,采用自然邻居插值确定同等级别的相邻单元信息,在此基础上建立了有限体积Godunov格式下的高性能自适应水流水质耦合模型。采用和谐浅水方程结合非负水深黎曼重构,同时给出非均匀结构网格下的源项离散格式,保证了模型的和谐性和稳定性;利用集成对流扩散通量的HLLC(Harten,Lax, van Leer and Contact)近似黎曼算子计算界面通量,配合不同等级单元间的通量交换公式,确保了模型的守恒性;根据梯度准则实现动态局部自适应网格,提出了满足守恒性的网格等级调整水流要素再分配方法。数值结果表明,相对于传统结构均匀网格模型,该模型兼顾精度与效率,能够高分辨率拟合复杂边界和捕捉计算敏感区域,准确反映复杂流态和物质的迁移扩散。
This paper presents a high-performance adaptive shallow water hydrodynamics-water quality coupling model in a second-order finite volume Godunov format that adopts dynamic local adaptive grid system combining natural neighbor interpolation to obtain the information of adjacent meshes at the same level. Wellbalanced shallow water equations with non-negative water depth reconstruction of Riemann states and proper discretization of source terms under the structured non-uniform grid are used to construct a well-balanced and stable model. The HLLC(Harten, Lax, van Leer and Contact) approximate Riemann solver with advectiondiffusion terms is utilized to calculate interface fluxes. The calculation formula of interface fluxes exchange among different level elements is applied to maintain the absolute conservative property. Dynamic local adaptive grid is achieved by gradient criterion. A flow information redistribution method corresponding to grid level adjustment which satisfies conservation laws is proposed. Numerical results show that the model not only captures sensitive areas and fits complex boundaries well, but also reflects complicated flow regime,transportation and diffusion laws accurately. Compared with the traditional structured uniform grid model, the proposed model has almost the same high-precision but better efficiency.
作者
郑川东
刘广宁
杨中华
荆平飞
王世昌
ZHENG Chuandong;LIU Guangning;YANG Zhonghua;JING Pingfei;WANG Shichang(State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University,Wuhan 430072,China;China Three Gorges Corporation,Yichang 443133,China;Wuhan Centre of China Geological Survey,Wuhan 430205,China)
出处
《武汉大学学报（工学版）》
CAS
CSCD
北大核心
2021年第9期784-794,共11页
Engineering Journal of Wuhan University
基金
自然资源部中国地质调查局地质调查项目(编号:DD20190263、202007000000180506)
国家自然科学基金项目(编号:51879199)。
关键词
结构非均匀网格
动态局部自适应
Godunov格式
梯度准则
水流水质耦合模型
计算效率
structured non-uniform grid
dynamic local adaptive
Godunov format
gradient criterion
hydrodynamics-water quality coupling model
computational efficiency
