【摘要】：對(duì)流擴(kuò)散方程是一類可以用來描述河流污染、大氣污染、污染物濃度,流體流動(dòng)以及熱傳導(dǎo)等眾多物理現(xiàn)象的運(yùn)動(dòng)方程.關(guān)于此類方程的有很多的求解方法,諸如有限元法、有限差分法、有限體積法等.其中最常見的數(shù)值方法之一就是有限差分法.因?yàn)槔幂^少網(wǎng)格點(diǎn)就容易構(gòu)造出高精度緊致格式,本文基于此分別在均勻網(wǎng)格與非均勻網(wǎng)格情況下構(gòu)造了相應(yīng)的差分格式,并驗(yàn)證所構(gòu)造格式的適用性和精確性,尤其是在對(duì)于大梯度、邊界層等問題的處理上顯示出一定的優(yōu)越性.本文針對(duì)對(duì)流擴(kuò)散方程問題展開分析,首先,針對(duì)所構(gòu)造的高精度緊致差分格式進(jìn)行簡(jiǎn)單的介紹,引入網(wǎng)格剖分函數(shù)后,分別在均勻與非均勻網(wǎng)格下構(gòu)造出格式,并通過數(shù)值算例驗(yàn)證格式的適用性與精確性;其次,基于Pade’逼近、Richardson外推法重構(gòu)出的高精度緊致格式,如此不但得到較高的計(jì)算精度且邊界條件易處理,穩(wěn)定性和計(jì)算結(jié)果的精確性也得到保證,也節(jié)省計(jì)算量;最后,將所構(gòu)造的高精度緊致差分格式運(yùn)用到水沙運(yùn)移的數(shù)值模擬當(dāng)中.為了便于進(jìn)行數(shù)值模擬,本文僅選取寧夏黃河大柳樹河段的近年的實(shí)測(cè)值與之進(jìn)行比較分析,從而驗(yàn)證方法的實(shí)用性與準(zhǔn)確性.
[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.
【學(xué)位授予單位】：北方民族大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.8

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 景何仿;李義天;李春光;;Numerical study of the flow in the Yellow River with non-monotonous banks[J];Journal of Hydrodynamics;2016年01期

2 王慧蓉;;求解對(duì)流擴(kuò)散方程的緊致差分方法[J];山西師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2015年03期

3 王慧蓉;;求解對(duì)流擴(kuò)散方程的緊致pade'逼近差分格式[J];數(shù)學(xué)的實(shí)踐與認(rèn)識(shí);2015年10期

4 尹治丹;陳建華;葛永斌;;求解二維擴(kuò)散方程的一種高精度緊致差分格式[J];四川師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2015年03期

5 黃雪芳;郭銳;葛永斌;;一維非定常對(duì)流擴(kuò)散方程非均勻網(wǎng)格上的高精度緊致差分格式[J];工程數(shù)學(xué)學(xué)報(bào);2014年03期

6 田芳;;非均勻網(wǎng)格上三維對(duì)流擴(kuò)散方程高精度緊致差分方法[J];寧夏大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年02期

7 肖建英;劉小華;李永濤;;非定常對(duì)流擴(kuò)散方程的高階差分格式[J];西南石油大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年03期

8 魏劍英;;二維定常對(duì)流擴(kuò)散方程的一種高精度緊致差分方法[J];重慶理工大學(xué)學(xué)報(bào)(自然科學(xué));2012年02期

9 王峰峰;王彩華;齊海濤;;二維對(duì)流擴(kuò)散方程的緊致差分格式[J];天津師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2011年01期

10 ;Numerical research on flow and thermal transport in cooling pool of electrical power station using three depth-averaged turbulence models[J];Water Science and Engineering;2009年03期

，

本文編號(hào)：2217870