【作者】 郭颂歌；

【导师】 金生；

【作者基本信息】 大连理工大学 ， 水力学及河流动力学， 2010， 硕士

【摘要】 河道和近海周围一直是人类的聚集之地,因此河道的演变对人类活动有很大影响,从而需要研究水流的运动规律来为人类服务,而数值模拟则是有效的研究方法之一。’在浅水动力学的研究中,出现很多较好的实用算法,例如一维的LAX-Wendroff显格式,Preissomann隐格式及特征差分格式,并通过算子分裂法或者ADI法将其应用到二维问题,这些方法可以应用到一定的场合,但对于实际的工程问题却不能完全尽人意。本文基于数值模拟方法中最有前景的有限体积法对二维浅水方程进行离散求解,建立了二维浅水模型,在模型的求解过程中,对数值通量的求解用Roe格式的近似黎曼解,使其能够处理强间断问题,求解中引入矩阵理论来处理系数矩阵；对源项的处理用迎风格式的特征方向法,使其在处理非平底问题时保证了界面通量上的平衡,并使格式具有高精度和稳定性。在挟沙水流问题的分析中,基于扩散理论用张洪武的考虑泥沙影响的流速沿垂线分布公式建立含沙量沿垂线分布的规律,克服应用比较广泛的罗斯公式中含沙量在水面处为0的弊端,分布状态更符合实际。另外在二维浅水方程的基础上增加了泥沙扩散方程和河床变形方程,对其耦合求解,从而模拟挟沙水流的运动规律及河床的冲淤变形情况。对比之前浅水动力学的方法,本文所建立的模型能够应用到工程实际中,在本文的最后一章用第二章所建立的二维浅水模型验证了实验室中两个有代表性的溃坝实验：方形非对称溃坝问题及带有三角形障碍物的溃坝问题,通过与实验室内的实测资料对比,其结果吻合良好,从而验证了二维浅水模型的准确性。用二维挟沙水流模型在不考虑冲淤的条件下模拟了温州海域内潮位场,流速场及含沙量变化过程,并与各个测站上实测资料的进行对比验证；对长江上沙市至监利段的水流运动规律进行数值模拟,在考虑冲淤及河床变形时,对其在一定时间段内的河床冲淤变形进行模拟验证。结果证明了模型在实际中的可应用性。更多还原

【Abstract】 The river’s surrounding and offshore have been the gathering place for human beings,so the evolution of the river will take a lot of affects for human being. It is necessary to research the law of water movement, and the numerical simulation is one of the effective ways within these methods.In the study of the shallow water, there are a lot of good practical algorithms, such as one-dimensional LAX-Wendroff、Preissomann format and characteristics of implicit difference scheme, and be applied to two-dimensional problem by operator splitting method or the ADI method. These methods can be applied to certain situations, but they are not fully intended the need of people for practical engineering problems.This article use the finite volume method to scatter the shallow water equation, and create the two-dimensional shallow water model, at the solving process of the model, pull in the approximate Riemann solution of Roe Format for obtaining numerical flux, to enable them to deal with discontinuous problems; at the question of deal with the source term, proposed the characteristic direction method of upwind format, to ensure the balance on the interface flux when deal with non-flat bottom, in the problem of the sediment analysis, based on diffusion theory, suspended sediment concentration variation along the vertical line which based on HongWu Zhang velocity distribution, this formula overcoming the shortcomings of 0 at the water surface, and the regular pattern is line with the practice. Then at the foundation of shallow water equation, add the diffusion equation and the bed deformation equation, simulating the movement of sediment and erosion deformation of the riverbed.Testing and verifying two experiment of dam break which did by some researchers in laboratory with the shallow water model:the dam break model of asymmetric square and the dam break model with triangular obstacle, by the contrast with the data of laboratory, proved the accurateness of the model.Simulated the sea of WenZhou with the model of sediment-laden flow, and contrast the tidemark、viocity and the sediment concentration with the data through measurement, then simulated the law of water movement and the erosion deformation of the riverbed between ShaShi and JianLi at Yangtze River. The result certificated the accurateness of the model.更多还原