本文選題：土壤水鹽運(yùn)移方程 + 有限點(diǎn)法��； 參考：《西安理工大學(xué)》2017年碩士論文

【摘要】：無(wú)網(wǎng)格法是在局部域上的節(jié)點(diǎn)處定義形函數(shù),能夠在計(jì)算區(qū)域任意增減節(jié)點(diǎn),克服了有限元法在數(shù)值計(jì)算中對(duì)網(wǎng)格的依賴。本文提出的有限點(diǎn)法屬于無(wú)網(wǎng)格法的一種,有限點(diǎn)法采用移動(dòng)最小二乘方法構(gòu)造形函數(shù),用配點(diǎn)法離散控制方程。對(duì)于土壤水鹽運(yùn)移模型中的對(duì)流-彌散模型,有限元法、有限差分法在對(duì)流占優(yōu)情況下容易產(chǎn)生震蕩,而有限點(diǎn)法在離散控制方程之前首先給控制方程施加穩(wěn)定項(xiàng),并在梯度變化較大的區(qū)域采用自適應(yīng)迎風(fēng)格式,可以有效的避免數(shù)值震蕩。本文主要的研究工作有如下幾個(gè)方面:首先,介紹了有限點(diǎn)法的基本原理和處理方法,包括移動(dòng)最小二乘形函數(shù)的構(gòu)造,權(quán)函數(shù)和支持域尺寸大小的選取方法、施加穩(wěn)定項(xiàng)原理、自適應(yīng)迎風(fēng)格式的應(yīng)用條件以及對(duì)控制方程的離散原則。其次,針對(duì)線性的一維、二維土壤鹽分運(yùn)移方程,構(gòu)造了有限點(diǎn)數(shù)值算法;針對(duì)非線性的一維、二維土壤水分運(yùn)動(dòng)方程,對(duì)計(jì)算過(guò)程中用到的顯式格式和隱式格式的處理方法做了介紹,構(gòu)造了有限點(diǎn)數(shù)值算法。最后,分別針對(duì)一維、二維土壤水分運(yùn)動(dòng)方程和土壤鹽分運(yùn)移方程進(jìn)行了數(shù)值模擬,深入討論了數(shù)值模擬結(jié)果與支持域大小、空間步長(zhǎng)和時(shí)間步長(zhǎng)之間的關(guān)系,并分析了收斂階和計(jì)算時(shí)間,進(jìn)而將數(shù)值模擬結(jié)果分別與有限元法、特征有限元和有限差分法進(jìn)行比較,說(shuō)明本文提出的有限點(diǎn)法是有效的。
[Abstract]:The meshless method defines the shape function at the nodes in the local domain. It can add or subtract nodes arbitrarily in the computational area and overcome the dependence of the finite element method on the mesh in the numerical calculation. The finite point method proposed in this paper belongs to the meshless method. The moving least square method is used to construct the shape function and the collocation method is used to discretize the governing equation. For the convection-dispersion model of soil water and salt transport model, the finite element method and the finite difference method are prone to oscillate in the case of convection, while the finite point method first applies a stable term to the governing equation before discretization of the governing equation. The adaptive upwind scheme is adopted in the regions with large gradient variation, which can effectively avoid numerical oscillation. The main research work of this paper is as follows: firstly, the basic principle and processing method of finite point method are introduced, including the construction of moving least square function, the selection of weight function and the size of support domain. The principle of stability, the application condition of adaptive upwind scheme and the principle of discretization of governing equations are given. Secondly, a finite point numerical algorithm is constructed for linear one-dimensional and two-dimensional soil salt transport equations, and for nonlinear one-dimensional and two-dimensional soil water motion equations, In this paper, the explicit and implicit schemes used in the calculation are introduced, and the finite point numerical algorithm is constructed. Finally, the one-dimensional and two-dimensional soil water motion equations and the soil salt transport equations are numerically simulated, and the relationship between the numerical simulation results and the size of the support domain, the space step and the time step is discussed. The convergence order and calculation time are analyzed, and the numerical simulation results are compared with the finite element method, the characteristic finite element method and the finite difference method, respectively. The results show that the finite point method proposed in this paper is effective.
【學(xué)位授予單位】：西安理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：S153;O241.82

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本文編號(hào)：1949140