Godunov格式下高精度二维水流-输运耦合模型  

A high-precision two-dimensional flow-transport coupled model based on Godunov's schemes

作　　者：毕胜[1,2] 周建中[1,2] 陈生水[3] 张华杰 刘懿[1,2] 赵越[1,2] 

机构地区：[1]华中科技大学水电与数字化工程学院,湖北武汉430074 [2]数字流域科学与技术湖北省重点实验室,湖北武汉430074 [3]南京水利科学研究院,江苏南京210029

出　　处：《水科学进展》2013年第5期706-714,共9页Advances in Water Science

基　　金：国家自然科学基金资助项目(51239004);水利部公益性行业科研专项经费资助项目(201001080)~~

摘　　要：针对复杂流体运动中物质输运方程的数值求解面临地形复杂、数值阻尼过大以及数值振荡等难题,建立了Godunov格式下求解二维水流-输运方程的高精度耦合数学模型,提出了集成输运对流项的HLLC(Harten-Lax-van Leer-Contact)型近似黎曼算子,可同时计算水流通量及输运通量,不仅有效模拟了复杂地形上水流运动,而且解决了输运方程中对流项产生的数值阻尼过大和不稳定振荡等难题。采用水深-水位加权重构技术和Minmod限制器,提高了模型处理复杂混合流态的能力,同时结合Hancock预测-校正方法,使模型具有时空二阶精度。算例结果表明,模型精度高、稳定性好,能有效抑制数值阻尼,适合模拟实际复杂流体运动中物质的输运过程,具有较好的推广应用价值。Numerical solution of flow-transport equations usually has to handle complex surface topography, numerical damping effect and numerical oscillation. In order to solve these problems, a high-performance Godunov-type finite volume model is proposed. An approximate Harten-Lax-van Leer-Contact （HLLC） Riemann solver for the integration of transport convection terms is used in the model development to calculate the mass fluxes and transport fluxes. The model can capture shock waves, reduce the numerical damping effect and overcome the numerical oscillation prob- lems. A weighted surface-depth gradient method and the Minmod limiter are used for water depth＇s reconstruction to improve the model accuracy. Moreover, the Hancock predictor-correetor method is adopted for time stepping. Numeri- cal results show that the proposed model is highly accurate and stable, and can significantly reduce the numerical damping effect. Thus, the model is suitable for simulating the transport problems in complex water flow and has a wide range of application potentials.

关 键 词：Godunov格式 水流-输运耦合模型 水深-水位加权变量重构技术 HLLC黎曼求解 Minmod限制器 

分 类 号：TV131.2[水利工程—水力学及河流动力学]