SIMPLE算法在潮流计算中的应用及改进研究
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摘要
本文在细致地考察了近年来有关水环境数值模拟方面研究成果的基础之上，采用控制体积法以及差分精度高的乘方定律格式离散二维水流数学模型，并在经典的SIMPLE算法的基础之上，通过总结前人对该算法的研究成果，从中选择科学、有效、简洁的方法对SIMPLE算法进行了改进的尝试。对改进后的算法，利用典型的方腔形流场比较了算法改进前后的计算结果。通过比较，发现改进后的算法具有更好的收敛速度。在此基础上，用C++语言编制了程序，对阳西海域潮流的运动规律进行了数值模拟研究，通过计算结果与实测数据的对比验证，得到了较好的模拟效果；同时利用阳西海域的实际计算过程验证了改进算法的有效性。
本文所提出的对SIMPLE算法的改进方法经过对方腔形流场以及阳西海域的验证计算，得到了较好的改进效果；对阳西海域数值模拟所得的结果可为阳西海域规划和环保工作提供可靠的数据支持，并为以后进一步研究该海域的污染物混合过程打下了良好的基础；论文所编制的程序亦可以用于其它宽浅型海域以及河流的二维数值模拟。
On the basis of carefully inspecting on the research about numerical simulation of water environment, this thesis adopted Control Volume Formulation and the Format of Involution Law which has high difference precision to disperse 2-D mathematics model of current; and on the basis of classical SIMPLE algorithm, by making a summary of the research on SIMPLE algorithm from former investigator, this thesis try to selected scientific, effective and laconic method to gain improvement on this algorithm. For the improved algorithm, using the result from typical quadrate cavity current area to compare the constringency speed of SIMPLE with the constringency speed of the improved algorithm. By comparing, finding that the improved SIMPLE algorithm has better constringency speed. On the basis of above, using the program of C++ to simulate the movement of tidal current in the maritime space of Yang Xi. By comparing the result of calculation with the result of observation, finding that the results are preferable; at the same time, the thesis has used the actual process of calculation in the maritime space of Yang Xi to prove the validity of improved algorithm.
By comparing the result with the result from quadrate cavity fluid area and the result of maritime space of Yang Xi, finding that the method which has been used to improve the SIMPLE algorithm in this thesis has preferable effect; the result of numerical simulation in the maritime space of Yang Xi can be used reliably for protecting and programming of the maritime space of Yang Xi, and for the ulterior research on the law of mixing of the pollutant; the program used in this article is also can be used for other sea areas and rivers which have more longer width than deepness.
本文所提出的对SIMPLE算法的改进方法经过对方腔形流场以及阳西海域的验证计算，得到了较好的改进效果；对阳西海域数值模拟所得的结果可为阳西海域规划和环保工作提供可靠的数据支持，并为以后进一步研究该海域的污染物混合过程打下了良好的基础；论文所编制的程序亦可以用于其它宽浅型海域以及河流的二维数值模拟。
On the basis of carefully inspecting on the research about numerical simulation of water environment, this thesis adopted Control Volume Formulation and the Format of Involution Law which has high difference precision to disperse 2-D mathematics model of current; and on the basis of classical SIMPLE algorithm, by making a summary of the research on SIMPLE algorithm from former investigator, this thesis try to selected scientific, effective and laconic method to gain improvement on this algorithm. For the improved algorithm, using the result from typical quadrate cavity current area to compare the constringency speed of SIMPLE with the constringency speed of the improved algorithm. By comparing, finding that the improved SIMPLE algorithm has better constringency speed. On the basis of above, using the program of C++ to simulate the movement of tidal current in the maritime space of Yang Xi. By comparing the result of calculation with the result of observation, finding that the results are preferable; at the same time, the thesis has used the actual process of calculation in the maritime space of Yang Xi to prove the validity of improved algorithm.
By comparing the result with the result from quadrate cavity fluid area and the result of maritime space of Yang Xi, finding that the method which has been used to improve the SIMPLE algorithm in this thesis has preferable effect; the result of numerical simulation in the maritime space of Yang Xi can be used reliably for protecting and programming of the maritime space of Yang Xi, and for the ulterior research on the law of mixing of the pollutant; the program used in this article is also can be used for other sea areas and rivers which have more longer width than deepness.
引文
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[19] 李国斌，韩信，天然河道淹没丁坝群水深平均平面二维数学模型研究，水动力学研究与进展，2001．6，A辑，16(2)：230～237．
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[30] 屈治国，何雅玲，陶文铨，求解流动和传热问题的一种新的全隐算法---CLEAR(上)，工程热物理学报，Jan．2005，Vol．26(1)：125-127．
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[39] 沈永明，吴修广，郑永红，曲线坐标下平面二维水流计算的代数应力湍流模型，水利学报，2005．4，Vol．36(4)：383-389．
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[2] Hansen, D.L.Yong, James.A.liggett, Transient finite element shallow lake circula-tion. J.Hydr.Divs.ASCE.HY2, 1977.
[3] 黄平，水环境数学模型及其应用，广州出版社，1996，117～136．
[4] 张青玉，黄河口潮流数值模拟，人民黄河，1994．1，(1)：9～14．
[5] 黄海，李琳，对流扩散方程的高精度差分有限元破开算子法，中山大学学报(自然科学版)，1996．3，35(2)：10～14．
[6] 陈小红，刘美南，海口市长流油气码头海域二维潮流数值模拟，中山大学学报(自然科学版)，1996，35(增刊)：78～84．
[7] 胡庆云，破开算子法用于二维流场计算的误差分析，河海大学学报，1999．1，27(1)：70～73．
[8] 詹杰民，边界拟合坐标系下的差分有限元破开算子法，力学学报，2002．7，34(4)：616～620．
[9] 张丽琼，崔广柏，肖俊英，长江江苏段水质模拟，水文，2002．6，22(3)：10～13．
[10] 赵枥华，李提来，陆家驹，长江江苏段二维水流—水质模拟，水利学报，2003．6，(6)：72～77．
[11] 赵枥华，戚晨，庾维德等，平面二维水流—水质有限体积法及黎曼近似解模型，水科学进展，2000．12，11(4)：368～374．
[12] 赵枥华等，姚琪，蒋艳等，通量向量分裂格式的二维水流—水质模拟，水科学进展，2002．11．13(6)：701～706．
[13] 魏根群，陈璧宏，宿晓辉，反调节水库非恒定流数值模拟，水科学进展，2001．12，11(4)：491～498．
[14] H. Abbassi, S. Turki, S. Ben Nasrallah, Interpolation functions in control volume finite element method, Computational Mechanics, 2003, (30): 303～309.
[15] 张华庆，乐培九，钦州港港区流场的数值模拟，水利水运科学研究，1994．6，(1、2)：81～88．
[16] 马福喜，李文新，河口水流、波浪、潮流、泥沙、河床变形二维数学模型，水利学报，1999．5，(5)：39～43．
[17] S. V. Patanka, D. H. Spalding., Calculation Procedure for Heat、Mass and Momentum Transfer in 3-D Flows[J]. Int. J. Heat Mass Transfer. 1972(15): 1787-1806．
[18] 李亚平，汤立群，陈界仁等，航道整治工程泥沙数学模型的构造及计算方法，水利水电技术，1999，30(12)：10～13．
[19] 李国斌，韩信，天然河道淹没丁坝群水深平均平面二维数学模型研究，水动力学研究与进展，2001．6，A辑，16(2)：230～237．
[20] 郭庆超，韩其为，何明民，二维潮流及泥沙数学模型，泥沙研究，1996．3，(1)：48～55．
[21] 李国斌，水电站枢纽坝区泥沙二维数模计算研究，水道港口，1994(3)：7～15．
[22] S. V. Patanka, Numerical heat transfer and fluid flow, [M]. New York, McGraw-Hill, 1980.
[23] S. V. Patanka, A calculation procedure for two-dimentional elliptic situation, [J]. Numer.Heat Transfer, 1981, 4 (4): 409—425.
[24] Da-Ren Chen and David Y. H. Pui, Numerical and experimental studies of particle deposition in a tube with a conical contraction—Laminar flow regime, Journal of Aerosol Science, June 1995, Volume 26 (4): 563-574.
[25] 李国斌，水电站枢纽坝区泥沙二维数模计算研究，水道港口，1994(3)：7-15．
[26] 李国斌，马进荣，三峡枢纽坝下通航水流条件平面二维数学模型研究，水利水电技术，1996，(4)：53-55．
[27] 李国斌，韩信，天然河道淹没丁坝群水深平均平面二维数学模型研究，水动力学研究与进展，2001．6，A辑，16(2)：230～237．
[28] 董耀华，河口潮流河段二维非恒定流数模研究及应用，长江科学院院报，Mar．1995，Vol．12(1)：31-39．
[29] 张宁，李光正，一种改进的SIMPLER算法，华中科技大学学报，Jun．2002，Vol．19(2)：28-31．
[30] 屈治国，何雅玲，陶文铨，求解流动和传热问题的一种新的全隐算法---CLEAR(上)，工程热物理学报，Jan．2005，Vol．26(1)：125-127．
[31] 陶文铨，数值传热学，西安交通大学出版社，1988．7：277-278．
[32] Van Doormal J. P. and Raithby G. D., Enhancement of SIMPLE Method for Predicting Incompressible Fluid Flows, [J]. Numer. Heat Transfer, 1984, (7): 147-163.
[33] 刘立军，徐忠，史峰等，大曲率弯道和页栅内的湍流数值模拟，空气动力学报，Jun．1997，Vol．15(2)：169-175．
[34] W. S. Zhang, Three-dimensional mathematical modeling of suspended sediment in the unsteady surface flow and non-linear evolution model of shallow wave in two-layer fluid, Postdoctoral Research Report, 1999, Wuhan University of Hydraulic and Electric Engineering.
[35] W. Z. Lu, W. S. Zhang, C. Z. Cui, A. Y. T. Leung, A numerical analysis of free-surface flow in curved open channel with velocity-pressure-free-surface correction, Computational Mechanics, February 2004, Vol. 33(3): 215-224.
[36] Y. Wang and S.Komori, On the improvement of the SIMPLE-like method for flows with complex geometry, Heat and Mass Transfer, Mar. 2000, Vol. 36(1): 71-78.
[37] 张华庆，李华国，岳翠平，海河口潮流泥沙运动数值模拟及清淤方案研究，水动力学研究与进展，Jun．2002，Ser．A，Vol．17(3)：318-325．
[38] 吴修广，沈永明，郑永红等，非正交曲线坐标下二维水流计算的SIMPLEC算法，水利学报，2003．2(2)：25-37．
[39] 沈永明，吴修广，郑永红，曲线坐标下平面二维水流计算的代数应力湍流模型，水利学报，2005．4，Vol．36(4)：383-389．
[40] Van Doormal J. P. and Raithby G. D., An Evaluation of the Segregated Approach for Predicting Incompressible Fluid Flows., ASME Paper 85-HT-9, 1985.
[41] Raithby G. D. and Schneider G. E., Elliptic System: Finite Difference Method Ⅱ [M]. In: W J Minkowycz, E M Sparrow, R H Pletcher, et al. Handbook of Numerical Heat transfer, John Wiley & Sona, New York, 1988, 241-289.
[42] 曾敏，陶文铨，密网格下SIMPLE登四种算法的收敛性与健壮性的比较，热科学与 技术，Mar．2003，Vol．2(1)：90-93．
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