基于自适应结构网格的二维浅水动力学模型  

Two-dimensional shallow hydrodynamic model based an adaptive structured grid

作　　者：张华杰 周建中[1] 毕胜[1] 宋利祥 

机构地区：[1]华中科技大学水电与数字化工程学院,武汉430074 [2]珠江水利科学研究院,广州510611

出　　处：《水动力学研究与进展（A辑）》2012年第6期667-678,共12页Chinese Journal of Hydrodynamics

基　　金：高等学校博士学科点专项科研基金资助项目(20100142110012);水利部公益性行业科研专项资助项目(201001080;201001034)~~

摘　　要：基于有限体积法建立了二维浅水动力学模型,提出了能够随着水波演进动态变化结构网格自适应算法,并依据网格自适应准则局部加密和消去网格,保证模型在计算效率与求解精度间取得平衡。空间上,采用水深-水位变量同时重构法定义界面底高程,引入梯度限制器策略,利用近似Riemann的HLLC型求解器计算界面数值通量;时间上,采用多步时间格式Runge-Kutta法。采用底坡项中心近似,并引入附加源项,保证数值格式的和谐性。运用改进的半隐式格式处理阻力源项,提高模型稳定性。经典型算例模拟结果表明,数值模型稳定性与和谐性较好,有较好的地形自适应能力,能够推广应用于复杂地形下水流计算。This paper presented an adaptive structured grid-based two-dimensional Godunov type finite-volume numerical model for unsteady shallow water flow, which can locally enrich and coarsen grids, and balance computation efficiency with solver accuracy. Conserved variables of water stage and water depth were reconstructed at the same time to define a uniquebottom of each cell interface. The HLLC approximate Riemann solver was adopted to calculate interface fluxes. Overall second order accuracy in space and in time was achieved by limiting gradients and using second order Runge-Kutta （RK2）. Bed source term was central discretization and extra flux term was added to obtain a well-balance scheme. Meanwhile the friction source term was treated in a semi-implicit way to reduce problems associated with numerical instabilities. Finally the presented model was validated by three benchmark tests and the results indicated that the model is well-balance, capture steep fronts well and simulate on complex topography stably and accurately.

关 键 词：二维浅水方程 自适应结构网格 Riemann求解器 Godunov格式 和谐性 

分 类 号：TV131.2[水利工程—水力学及河流动力学]