改进型WENO格式及其对溃坝流的高精度数值模拟  

High-accuracy numerical simulations on dam break flows with improved WENO scheme

作　　者：李小纲 李国栋[1] 葛永斌[2] LI Xiao-gang;LI Guo-dong;GE Yong-bin(State Key Laboratory of Eco-hydraulics in Northwest Arid Region,Xi'an University of Technology,Xi'an 710048 China;Institute of Applied Mathematics and Mechanics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]西安理工大学省部共建西北旱区生态水利国家重点实验室,西安710048 [2]宁夏大学应用数学与力学研究所,银川750021

出　　处：《水动力学研究与进展（A辑）》2019年第4期512-519,共8页Chinese Journal of Hydrodynamics

基　　金：陕西水利科技计划项目(2017slkj-17);陕西省重点研发计划项目(2018SF-352)~~

摘　　要：该文基于浅水波方程组建立一维溃坝洪水模型,通过对经典WENO格式(WENO-JS)计算模板重组得到相应的两个二次多项式和一个四次多项式,对其进行加权处理得到一个改进的WENO格式(WEMO-P)。该格式中大模板的光滑因子形式比较复杂,对两个小模板光滑因子进行加权组合,代替大模板光滑因子,得到一个光滑因子改进后的WENO格式(WENO-P-N)。理论分析与数值结果表明:WEMO-P和WENO-P-N格式与WENO-JS格式在光滑区域可达相同阶的计算精度,但在相同网格下,WEMO-P和WENO-P-N格式求解具有更小的截断误差,能够更有效地减弱数值振荡,对间断具有更高的分辨率,WENO-P-N格式比WENO-P格式的计算时间更小,因此WENO-P-N格式的计算效率最高。并对一维溃坝水流进行数值模拟研究,验证了该方法的实用性和有效性。This paper presents a model of one-dimensional dam break flows based on shallow water equation. An improved WENO scheme(WENO-P) is constructed by weighted combination of two quadratic polynomials and a fourth-degree polynomial,which are deserved from the classical WENO(WENO-JS) computational stencils. The explicit form of smoothness indicator for big stencil is difficult, another improved WENO scheme(WENO-P-N) is obtained by weighting the smoothness indicators of the small stencils. Theoretical analysis and numerical results show the WENO-P scheme and WENO-P-N scheme can reach the same convergence order of WENO-JS;while it can obtain smaller truncation errors at smooth parts of the solution and higher resolution close to the discontinuities than the WENO-JS. On the same grids, the computational time of WENO_P-N scheme is less than WENO-P scheme, so WENO-P-N scheme is the most efficient. Finally, one-dimensional dame break flow is simulated by the improved scheme, the practicability and the validity of the improved scheme is verified.

关 键 词：溃坝流 WENO格式 数值模拟 浅水方程 

分 类 号：O175.2[理学—数学]