水体交换年龄模型研究
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摘要
采用剖开算子法,把水体年龄控制方程分成几个连续的初值问题。在任意三角形网格中,分别对不同性质的算子采用各自适合的算法,即采用特征线法求解对流分步,采用半隐式有限元法求解扩散分步和传播分步。利用水体交换模型试验结果和水体年龄对称特性解析解对所建立的年龄模型进行了验证计算,结果表明,建立的水体年龄模型计算结果与试验结果、解析解结果吻合,可较好地预测水体交换年龄。
2-D water age model by operator-splitting algorithm is developed. The governing equation is splitted into three or two successive initial value problems. In any arbitrary triangle calculation grid,the operators are calculated by different algorithm on the basis of their characteristics. In convection problem,the method of characteristics is used. For the dispersion and propagation problem,a semi-implicit finite element algorithm is employed in the calculation. The model validation is tested by two different ways,including establishing a water transfer physical model and analytic solutions based on the symmetry characteristic of age model. The computed results well agree with the two tests,including velocity,concentration and age. This study can provide technical support for the age model validation.
2-D water age model by operator-splitting algorithm is developed. The governing equation is splitted into three or two successive initial value problems. In any arbitrary triangle calculation grid,the operators are calculated by different algorithm on the basis of their characteristics. In convection problem,the method of characteristics is used. For the dispersion and propagation problem,a semi-implicit finite element algorithm is employed in the calculation. The model validation is tested by two different ways,including establishing a water transfer physical model and analytic solutions based on the symmetry characteristic of age model. The computed results well agree with the two tests,including velocity,concentration and age. This study can provide technical support for the age model validation.
引文
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[15]邵军荣,吴时强,周杰,等.二维输运方程高精度数值模拟[J].水科学进展,2012,23(3):383-389.(SHAO Junrong,WU Shiqiang,ZHOU Jie,et al.High accuracy numerical simulation for 2-D transportation problem[J].Advances in Water Science,2012,23(3):383-389.(in Chinese))
[16]周杰,汪德爟.有限元水流计算中内存和运行效率初探[J].水科学进展,2004,15(5):593-597.(ZHOU Jie,WANG Deguan.Exploration on memory requirement and operation efficiency of finite element method in flow caculation[J].Advances in Water Science,2004,15(5):593-597.(in Chinese))
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[18]SHEN J,WANG H V.Determining the age of water and long-term transport timescale of the Chesapeake Bay[J].Estuarine,Coast-al and Shelf Science,2007,74(4):585-598.
[19]SKOOG D A,WEST D M,HOLLER F J,et al.Fundamentals of analytical chemistry[M].New York:[s.n.],1988.
[20]丁道扬,吴时强.三维宽浅河道水流数学模型研究[J].中国工程科学,2010,12(2):31-39.(DING Daoyang,WU Shiqiang.Study on three-dimensional numerical model for shallow water flow[J].Engineering Sciences of China,2010,12(2):31-39.(in Chinese))
[2]DELHEZ E,CAMPIN J M,HIRST A C,et al.Toward a general theory of the age in ocean modelling[J].Ocean Modelling,1999,1(1):17-27.
[3]DELEERSNIJDER E,CAMPIN J M,DELHEZ E.The concept of age in marine modelling:I:Theory and preliminary model results[J].Journal of Marine Systems,2001,28:229-267.
[4]BECKERS J M,DELHEZ E,DELEERSNIJDER E.Some properties of generalized age-distribution equations in fluid dynamics[J].Journal of Applied Mathematics,2001,61(5):1526-1544.
[5]HIRST A C.Determination of water component age in ocean models:Application to the fate of North Atlantic Deep Water[J].Ocean Modelling,1999,1(2):81-94.
[6]DELHEZ E,DELEERSNIJDER E.The concept of age in marine modelling:Ⅱ:Concentration distribution functions in the English Channel and the North Sea[J].Journal of Marine Systems,2002,31(4):279-297.
[7]DELHEZ E,DELEERSNIJDER E,MOUCHET A,et al.A note on the age of radioactive tracers[J].Journal of Marine Systems,2003,38(3/4):277-286.
[8]HALL T M,HAINE W N.Tracer age symmetry in advective-diffusive flows[J].Journal of Marine Systems,2004,48(1/2/3/4):51-59.
[9]SHEN J,HAAS L.Calculating age and residence time in the tidal York River using three-dimensional model experiments[J].Estuarine,Coastal and Shelf Science,2004,61(3):449-461.
[10]GOURGUE O,DELEERSNIJDER E,WHITE L.Toward a generic method for studying water renewal,with application to the epilimnion of Lake Tanganyika[J].Estuarine,Coastal and Shelf Science,2007,74(4):628-640.
[11]ZHANG W G,WILKIN J L,SCHOFIELD O M.Simulation of water age and residence time in New York Bight[J].Journal of Physical Oceanography,2010,40(5):965-981.
[12]LI Y P,ACHARYA K,CHEN D,et al.Modeling water ages and thermal structure of Lake Mead under changing water levels[J].Lake and Reservoir Management,2010,26:258-272.
[13]LI Y P,ACHARYA K,YU Z B.Modeling impacts of Yangtze River water transfer on water ages in Lake Taihu,China[J].Ecological Engineering,2011,37(2):325-334.
[14]邵军荣.太湖湖区水量交换与水质变化规律研究及应用[D].南京:南京水利科学研究院,2013:19-38.(SHAO Junrong.The laws and application research on water quantity and water quality exchange in the Taihu Lake area[D].Nanjing:Nanjing Hydraulic Research Institute,2013:19-38.(in Chinese))
[15]邵军荣,吴时强,周杰,等.二维输运方程高精度数值模拟[J].水科学进展,2012,23(3):383-389.(SHAO Junrong,WU Shiqiang,ZHOU Jie,et al.High accuracy numerical simulation for 2-D transportation problem[J].Advances in Water Science,2012,23(3):383-389.(in Chinese))
[16]周杰,汪德爟.有限元水流计算中内存和运行效率初探[J].水科学进展,2004,15(5):593-597.(ZHOU Jie,WANG Deguan.Exploration on memory requirement and operation efficiency of finite element method in flow caculation[J].Advances in Water Science,2004,15(5):593-597.(in Chinese))
[17]PRESS W H,TEUKOLSKY S A,VETTERLING W T,et al.Numerical recipes in fortran77:The art of scientific computing[M].Cambridge:Cambridge University Press,1992:71-82.
[18]SHEN J,WANG H V.Determining the age of water and long-term transport timescale of the Chesapeake Bay[J].Estuarine,Coast-al and Shelf Science,2007,74(4):585-598.
[19]SKOOG D A,WEST D M,HOLLER F J,et al.Fundamentals of analytical chemistry[M].New York:[s.n.],1988.
[20]丁道扬,吴时强.三维宽浅河道水流数学模型研究[J].中国工程科学,2010,12(2):31-39.(DING Daoyang,WU Shiqiang.Study on three-dimensional numerical model for shallow water flow[J].Engineering Sciences of China,2010,12(2):31-39.(in Chinese))