高精度紧致格式在水沙运移数值模拟中的应用

发布时间：2018-09-01 17:25

【摘要】：对流扩散方程是一类可以用来描述河流污染、大气污染、污染物浓度,流体流动以及热传导等众多物理现象的运动方程.关于此类方程的有很多的求解方法,诸如有限元法、有限差分法、有限体积法等.其中最常见的数值方法之一就是有限差分法.因为利用较少网格点就容易构造出高精度紧致格式,本文基于此分别在均匀网格与非均匀网格情况下构造了相应的差分格式,并验证所构造格式的适用性和精确性,尤其是在对于大梯度、边界层等问题的处理上显示出一定的优越性.本文针对对流扩散方程问题展开分析,首先,针对所构造的高精度紧致差分格式进行简单的介绍,引入网格剖分函数后,分别在均匀与非均匀网格下构造出格式,并通过数值算例验证格式的适用性与精确性;其次,基于Pade’逼近、Richardson外推法重构出的高精度紧致格式,如此不但得到较高的计算精度且边界条件易处理,稳定性和计算结果的精确性也得到保证,也节省计算量;最后,将所构造的高精度紧致差分格式运用到水沙运移的数值模拟当中.为了便于进行数值模拟,本文仅选取宁夏黄河大柳树河段的近年的实测值与之进行比较分析,从而验证方法的实用性与准确性.
[Abstract]:Convection-diffusion equation is a kind of motion equation which can be used to describe many physical phenomena such as river pollution, air pollution, pollutant concentration, fluid flow and heat conduction. There are many methods for solving such equations, such as finite element method, finite difference method, finite volume method and so on. One of the most common numerical methods is the finite difference method. Because it is easy to construct a compact scheme with high accuracy by using fewer mesh points, the difference scheme is constructed in the case of uniform mesh and non-uniform mesh respectively, and the applicability and accuracy of the scheme are verified. Especially in the large gradient, boundary layer and other problems show some advantages. In this paper, the problem of convection-diffusion equation is analyzed. Firstly, the compact difference scheme with high precision is introduced. After introducing the mesh generation function, the scheme is constructed under uniform and non-uniform meshes, respectively. The applicability and accuracy of the scheme are verified by numerical examples. Secondly, the high precision compact scheme is reconstructed based on the Pade' approximation Richardson extrapolation method, which not only obtains higher calculation accuracy, but also the boundary conditions are easy to deal with. The stability and accuracy of the calculation results are also guaranteed, and the computational complexity is saved. Finally, the high precision compact difference scheme is applied to the numerical simulation of water and sediment transport. In order to carry on the numerical simulation, this paper only selects the Ningxia Yellow River Daliushu River in recent years to carry on the comparison analysis with it, thus verifies the practicability and the accuracy of the method.
【学位授予单位】：北方民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8

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