强不规则地形上浅水二维流动的数值计算研究  

Numerical modeling of shallow flows over irregular topography

作　　者：王鑫[1] 曹志先[1] 岳志远[1] 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,湖北武汉430072

出　　处：《水动力学研究与进展（A辑）》2009年第1期56-62,共7页Chinese Journal of Hydrodynamics

基　　金：国家重点基础研究发展(973)计划(2007CB714106)资助

摘　　要：浅水流动数值模拟技术取得了显著进步,已能够有效地捕捉激波,但是应用于强不规则地形时计算困难,其原因在于:陡峭坡面上水流重力作用对数值稳定性有重要影响。采用简单的算子分裂法,即使是时间步长满足CFL稳定性准则,也可能致使计算不稳定,或者要求远比CFL稳定性准则更加苛刻的时间步长,从而严重影响计算效率。本文建立对强不规则地形和一般地形条件均能保持高效率的浅水二维数学模型:基本控制方程采用二维浅水方程;在空间上采用能捕捉激波的WAFTVD二阶精度格式;在时间上采用三阶TVD龙格库塔法,并采用自适应步长满足数值稳定性要求。将该模型应用于冰湖溃决洪水的模拟,试验结果表明:该文模型从本质上解除了强不规则地形对时间步长的约束,与现有数学模型相比,计算效率达到数量级上的提高,为强不规则地形上浅水二维流动数值模型的广泛应用(如高原与山丘区溃坝洪水数值预报等)提供了新的技术基础。While significant progresses have been achieved in recent decades in solving the hyperbolic equations of shallow water flows, which could accommodate shock waves, computational difficulty arises from the highly irregular topography in mountainous areas. In particular, under a simple operator-splitting framework, a very small time step （or Courant number） is found to be necessary for stability, and this is dictated by the magnitude of the source terms in relation to the highly irregular topography and significantly increases the computational cost. Here an efficient shock-capturing finite volume algorithm is presented for solving the hyperbolic equations of shallow water flows. It is based on a splitting scheme, a spatially second-order WAF-TVD method along with the HLL approximate Riemann solver, and a temporally third-order TVD Runge-Kutta scheme. In order to satisfy the numerical stability, a self-adaptable time step method is proposed under the Runge-Kutta scheme. Application of the model to the prediction of flooding due to sudden outburst of a real glacial-lake is evaluated. It is found that the present model is essentially free from the restriction on time step arising from highly irregular topography. Compared with previous models, the computational efficiency of the model is significantly enhanced.

关 键 词：强不规则地形 浅水流动 数值稳定性 自适应时间步长 计算效率 

分 类 号：TV131.2[水利工程—水力学及河流动力学]