本文關(guān)鍵詞：多孔介質(zhì)中Darcy-Forchheimer模型的多重網(wǎng)格方法　出處：《山東大學(xué)》2017年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Darcy-Forchheimer模型 混合元 多重網(wǎng)格方法 Peaceman-Rachford迭代 數(shù)值實(shí)驗(yàn)

【摘要】：多孔介質(zhì)中流體流動(dòng)的數(shù)學(xué)物理模型廣泛應(yīng)用于描述油藏開發(fā)過程中[6][9][57]。多孔介質(zhì)中的流體運(yùn)動(dòng)所遵循的基本規(guī)律都是建立在質(zhì)量守恒、動(dòng)量守恒和能量守恒基礎(chǔ)之上的。油藏研究的目的就是預(yù)測(cè)油藏未來走向動(dòng)態(tài),找到提高最終采收律的方法和途徑。將需要模擬的物理系統(tǒng)用適當(dāng)?shù)臄?shù)學(xué)方程表示,這個(gè)過程一般都作必要的假設(shè)條件。從實(shí)際的觀點(diǎn)來說,為了使問題易于處理,這種假設(shè)是必須的。構(gòu)成油藏?cái)?shù)學(xué)模型的方程組一般都比較復(fù)雜,不能用解析的方法求解。所以必須要在計(jì)算機(jī)上近似求解。而在計(jì)算機(jī)上數(shù)值模擬油藏之前,需要建立油藏的數(shù)學(xué)模型。多孔介質(zhì)中流體流動(dòng)的物理模型在數(shù)學(xué)上表現(xiàn)為依賴于時(shí)間的強(qiáng)耦合的非線性偏微分方程組。由于多孔介質(zhì)中這類模型十分復(fù)雜,流體運(yùn)動(dòng)所遵守的質(zhì)量守恒集中體現(xiàn)物質(zhì)的平衡,實(shí)際生產(chǎn)中表現(xiàn)為注產(chǎn)體積以及質(zhì)量的平衡;而動(dòng)量守恒主要是對(duì)速度與壓力的關(guān)系式的描述;實(shí)際生產(chǎn)中主要關(guān)心物質(zhì)的平衡和壓力分布。所以需要進(jìn)一步地引入各種假設(shè)對(duì)模型進(jìn)行簡(jiǎn)化,降低耦合性、非線性強(qiáng)度。比如作為經(jīng)驗(yàn)公式引入的Darcy定律以及其他非Darcy律,以及假設(shè)流體不可壓或者微可壓等等。假設(shè)流體不可壓縮,化簡(jiǎn)的質(zhì)量守恒方程和速度壓力的Darcy定律耦合是常用的數(shù)學(xué)模型,可以將速度消去,求解只含有壓力的橢圓方程。如果假設(shè)流體微可壓縮,引入微可壓縮系數(shù),化簡(jiǎn)的質(zhì)量守恒方程和Darcy定律耦合,將速度消去,則得到只有壓力的拋物方程。若不消去速度,可以直接對(duì)混合弱形式構(gòu)造逼近格式,其中dual型格式參考文獻(xiàn)主要有[16][17][18][26][51][52]。primal型格式可以參考[28] [74]。Darcy定律主要描述流體流速u和壓力p的梯度之間的線性關(guān)系,描述了多孔介質(zhì)中Newton流體的滲流現(xiàn)象。當(dāng)Darcy速度u特別小的時(shí)候,Darcy定律才成立[6]。Forchheimer在1901年觀察到當(dāng)Reynolds數(shù)比較大(大致Re 1)[38]時(shí),壓力梯度與速度之間存在非線性關(guān)系。Forchheimer模型推導(dǎo)或經(jīng)驗(yàn)公式的工作可以參考[66][77][21][2][35][43]。Forchheimer方程數(shù)學(xué)理論方面的工作可以參考[66][31][69]。Forchheimer方程本質(zhì)上是一類非線性單調(diào)非退化方程,類似的問題還有p-Laplacian問題,擬Newtion問題,處理這一類單調(diào)非線性問題的技巧和方法可以參考[30][29][32][33]。一般這類數(shù)學(xué)模型的偏微分方程組結(jié)構(gòu)比較復(fù)雜,耦合求解難度大。同時(shí)因?yàn)槎嗫捉橘|(zhì)類型多樣,尺度變化大,導(dǎo)致數(shù)值模擬計(jì)算量大,收斂速度較慢。所以運(yùn)用計(jì)算機(jī)對(duì)這類數(shù)學(xué)模型進(jìn)行大規(guī)模、快速保精度的數(shù)值求解成為科學(xué)與工程中的迫切需求。近些年來,已經(jīng)有了很多關(guān)于Darcy-Forchheimer模型的數(shù)值分析工作。其中Girault和Wheeler在[38]中已經(jīng)通過證明非線性算子A(v)=μ/σK-1v+β/ρ|v|v的單調(diào)性、強(qiáng)制性以及半連續(xù)性,從而證明了 Darcy-Forchheimer模型解的存在唯一性,同時(shí)給出了一個(gè)合適的inf-sup條件。然后他們考慮分別用分片常數(shù)和非協(xié)調(diào)Crouzeix-Raviart混合元來逼近速度和壓力。他們證明了離散的inf-sup條件以及給出的混合元格式的收斂性。同時(shí)他們用Peaceman-Rachford [58]類型的迭代方法來求解離散的非線性代數(shù)方程,并給出了這類迭代法的收斂性。在Peaceman-Rachford迭代方法中,非線性方程通過和散度方程解耦,然后求解一個(gè)封閉的方程。Lopez,Molina, Salas在[49]中實(shí)現(xiàn)了文獻(xiàn)[38]中所提方法的數(shù)值實(shí)驗(yàn),并且針對(duì)Newton法和Peaceman-Rachford迭代方法求解非線性方程做了對(duì)比。他們指出對(duì)比Peaceman-Rachford迭代方法求解非線性方程,Newton法求解非線性方程并沒有優(yōu)勢(shì)。因?yàn)樵诿恳徊降?Newton法需要求解一個(gè)Jacobian矩陣,然后再求解一個(gè)線性鞍點(diǎn)系統(tǒng),但是在Peaceman-Rachford迭代中,只需要針對(duì)解耦之后的非線性方程計(jì)算一個(gè)人為引入的中間值,然后求解一個(gè)簡(jiǎn)化的線性鞍點(diǎn)問題。對(duì)比形成一個(gè)Jacobian矩陣所需要的工作量,求解解耦之后的非線性方程消耗的工作量可以忽略不計(jì)。而且,在選取同樣的迭代初值的條件下,Peaceman-Rachford迭代比Newton法收斂所需的迭代步數(shù)少。細(xì)節(jié)可以參考文獻(xiàn)[49]。Park在文獻(xiàn)[56]中對(duì)時(shí)間依賴的Darcy-Forchheimer模型提出了一種半離散的混合元格式。Pan和Rui在文獻(xiàn)[54]中對(duì)Darcy-Forchheimer模型給出了一種基于 Raviart-Thomas (RT)元或者 Brezzi-Douglas-Marini (BDM)元逼近速度,分片常數(shù)逼近壓力dual形式的混合元方法。他們將Darcy-Forchheimer 模型中速度化為壓力梯度的函數(shù), 得到了一個(gè)非線性單調(diào)只含壓力的橢圓偏微分方程,并且基于單調(diào)非退化方程的正則性證明了連續(xù)和離散問題的inf-sup條件,證明了解的存在唯一性。最后用Darcy-Forchheimer算子的單調(diào)性給了速度L2,L3范數(shù),壓力L2范數(shù)的先驗(yàn)誤差估計(jì)。Rui和Pan在文獻(xiàn)[63]中給出了 Darcy-Forchhcimer模型的塊中心有限差分方法,其中塊中心有限差分在合適的數(shù)值積分公式下可以認(rèn)為是最低階的RT-P0混合元方法。Rui, Zhao和Pan在文獻(xiàn)[64]中針對(duì)Darcy-Forchheimer模型中的Forchheimer系數(shù)是變量的情況,即β(x),給出了相應(yīng)的塊中心有限差分方法。Wang和Rui在文獻(xiàn)[76]中對(duì)Darcy-Forchheimer模型構(gòu)造了一種穩(wěn)定的Crouzeix-Raviart混合元方法。Rui和Liu在文獻(xiàn)[62]中對(duì)Darcy-Forchheimer模型介紹了一種二重網(wǎng)格塊中心有限差分方法。Salas, Lopez,和Molina在文獻(xiàn)[67]中給出了他們?cè)谖墨I(xiàn)[49]中實(shí)現(xiàn)的混合元方法的理論分析,并給出了解的適定性分析和收斂性證明。上述提到的大多數(shù)前人的工作主要致力于對(duì)Darcy-Forchheimer模型的離散方法。除了在文獻(xiàn)[38]中提到的Peaceman-Rachford迭代法,很少有工作探索針對(duì)離散后得到的非線性鞍點(diǎn)問題的快速解法,而這正是本篇論文的出發(fā)點(diǎn)和主題。多重網(wǎng)格方法是許多高效求解線性和非線性橢圓問題的方法之一。需要特別指出的事,對(duì)非線性問題,我們不會(huì)再得到一個(gè)簡(jiǎn)單的線性殘量方程,這就是處理線性和非線性問題的最重要的區(qū)別。這里我們所用的多重網(wǎng)格格式是我們常用來處理非線性問題的多重網(wǎng)格方法,稱為全近似格式(FAS) [20]。因?yàn)槲覀冊(cè)谇蠼獯志W(wǎng)格的問題時(shí)用的是全近似,而不是只用誤差。本文對(duì)多孔介質(zhì)中Darcy-Forchheimer模型構(gòu)造了基于協(xié)調(diào)和非協(xié)調(diào)混合元方法離散分別給出了有效的非線性多重網(wǎng)格方法。我們用Peaceman-Rachford迭代法作為多重網(wǎng)格方法中的光滑子來解耦非線性方程和質(zhì)量守恒方程。我們把線性的鞍點(diǎn)問題簡(jiǎn)化成一個(gè)對(duì)稱正定的問題求解,并且說明了我們這種處理方式的有效性。針對(duì)用來解耦非線性方程和限制條件的分裂參數(shù)α,文獻(xiàn)[49]中對(duì)Forchheimer系數(shù)β不同的取值,總是取α = 1,而我們找到了一個(gè)更好的值,并且通過比較迭代收斂需要的次數(shù)和CPU計(jì)算時(shí)間說明了我們?nèi)〉闹蹈�。我們做了很多�?shù)值實(shí)驗(yàn)來說明我們構(gòu)造的多重網(wǎng)格求解器的有效性。我們構(gòu)造的方法收斂即不依賴于離散網(wǎng)格的大小也不依賴于Forchheimer數(shù)的取值,并且我們的計(jì)算復(fù)雜度是接近于線性的。需要提醒的是,構(gòu)造一個(gè)快速算法不依賴于一些重要的參數(shù)是一件不容易的事情,例如文獻(xiàn)[50, 53]中對(duì)一類線性Stokes方程的處理。本文組織結(jié)構(gòu)如下:第一章,簡(jiǎn)要介紹了多孔介質(zhì)中Darcy-Forchheimer方程及其適用范圍,以及質(zhì)量守恒定律及其在各種假設(shè)下的變形,本文所處理的數(shù)學(xué)模型,求解的方程組就是基本方程的耦合。第二章,簡(jiǎn)要回顧了求解離散方程的基本數(shù)值計(jì)算方法。包括線性方程組的直接解法以及線性迭代解法和非線性迭代解法。除了介紹不同的數(shù)值方法外,還簡(jiǎn)要概述了每種方法有效適用的情況。同時(shí)說明了基礎(chǔ)迭代法的優(yōu)勢(shì)和缺陷。經(jīng)典的迭代法本質(zhì)上僅起到“光滑”作用,即它能很快地消去殘量中的高頻部分,但對(duì)低頻部分,效果卻不是很好。以經(jīng)典迭代法求解齊次Dirichlet邊界的二維Poisson問題為例來說明迭代法的光滑性質(zhì)。第三章,介紹了多重網(wǎng)格方法最基本的思想和最基礎(chǔ)的算法。首先介紹了線性多重網(wǎng)格方法,因?yàn)閷?duì)線性問題誤差滿足殘量方程,但是它對(duì)非線性問題并不適用,對(duì)非線性問題,則需要采取不同的策略。隨之介紹了兩種常見的非線性多重網(wǎng)格方法。第四章,對(duì)多孔介質(zhì)中Darcy-Forchheimer模型構(gòu)造了基于協(xié)調(diào)混合元方法離散給出了一種有效的非線性多重網(wǎng)格方法。我們用Peaceman-Rachford迭代法作為多重網(wǎng)格方法中的光滑子來解耦非線性方程和質(zhì)量守恒方程。我們把線性的鞍點(diǎn)問題簡(jiǎn)化成一個(gè)對(duì)稱正定的問題求解,并且我們說明了我們這種處理方式的有效性。針對(duì)用來解耦非線性方程和限制條件的分裂參數(shù)α,文獻(xiàn)[49]中對(duì)Forchheimer系數(shù)β不同的取值,總是取α= 1,而我們找到了一個(gè)更好的值,并且通過比較迭代收斂需要的次數(shù)和CPU計(jì)算時(shí)間說明了我們?nèi)〉闹蹈�。我們做了很多�?shù)值實(shí)驗(yàn)來說明我們構(gòu)造的多重網(wǎng)格算法的有效性。我們構(gòu)造的方法收斂即不依賴于離散網(wǎng)格的大小也不依賴于Forchheimer系數(shù)的取值,并且我們的計(jì)算復(fù)雜度是接近于線性的。本部分內(nèi)容出自文章[42],該文章已在期刊Journal of Scientific Computing(SCI)在線發(fā)表。第五章,對(duì)多孔介質(zhì)中Darcy-Forchheimer模型構(gòu)造了基于非協(xié)調(diào)混合元方法離散給出了一種有效的非線性多重網(wǎng)格方法。非協(xié)調(diào)混合元多重網(wǎng)格和協(xié)調(diào)混合元多重網(wǎng)格相比最重要的區(qū)別是離散空間不嵌套,因此在對(duì)網(wǎng)格函數(shù)在不同網(wǎng)格之間的轉(zhuǎn)換時(shí),我們不能再由簡(jiǎn)單的自然映射得到。關(guān)鍵的問題就是如何來構(gòu)造網(wǎng)格之間的投影算子。和協(xié)調(diào)多重網(wǎng)格方法一樣,我們做了很多數(shù)值實(shí)驗(yàn)來說明我們構(gòu)造的多重網(wǎng)格算法的有效性。我們構(gòu)造的方法收斂即不依賴于離散網(wǎng)格的大小也不依賴于Forchheimer系數(shù)的取值,并且我們的計(jì)算復(fù)雜度是接近于線性的。
[Abstract]:Wide application of mathematical and physical model of fluid flow in porous media in the basic law is described by [6][9][57]. fluid flow in porous media in the process of reservoir development are established on the basis of mass conservation, momentum conservation and energy conservation. The purpose of the study is to predict the reservoir dynamic trend of reservoir, to improve the ultimate recovery method and way of law the physical simulation system. The needs expressed by appropriate mathematical equations, this process is generally assumed conditions necessary. From the practical point of view, in order to make the problem tractable, this assumption is necessary. A mathematical model of reservoir equations is generally more complex, can not be solved by analytical method. Must be the approximate solution on the computer. Before the computer numerical reservoir simulation, mathematical model to establish reservoir fluid flow in porous media. The physical model of dynamic performance for strong coupling nonlinear time dependent partial differential equations in mathematics. Because of this kind of porous medium model is very complex, the mass conservation of fluid motion in accordance with the embodiment of the material balance, performance for the injection production volume and quality balance in actual production; and the momentum is the velocity and pressure of the description; the actual production is mainly concerned about material balance and pressure distribution. So it is necessary to further introduce various assumptions to simplify the model, reduce the coupling strength. For example, the nonlinear Darcy law as the empirical formula and other non Darcy law, and assuming that the fluid is incompressible or micro pressure wait. If the fluid is incompressible, the Darcy coupling law of mass conservation equation and the rate of pressure reduction is a commonly used mathematical model, the speed can be deleted, which contains only solution Elliptic equation of pressure. If the assumption of slightly compressible fluid, the slightly compressible coefficient, mass conservation equation and Darcy law coupling simplification, the speed of elimination, is parabolic pressure. If not only the elimination rate, can be directly on the mixed weak form approximate lattice type, the dual type main reference format [16][17][18][26][51][52].primal format can refer to [28] [74].Darcy's law describes the linear relationship between the fluid velocity and pressure gradient of u p, describes the seepage phenomenon of Newton fluid in the porous medium. When the speed of Darcy u small, Darcy law was established in 1901 [6].Forchheimer was observed when the Reynolds number is large (approximately 1 Re) [38] when there is a nonlinear relationship.Forchheimer model or empirical formula between pressure gradient and velocity of the work can refer to [66][77][21][2][35][43].Forchhe The IMER equation theory can be found in the [66][31][69].Forchheimer equation is essentially a nonlinear monotone non degenerate equations, there are similar problems to p-Laplacian problem, Newtion problem, skills and methods of dealing with this type of monotone nonlinear problems can refer to [30][29][32][33]. this kind of general mathematical model of partial differential equations with complex structure, coupling at the same time difficult. Because the porous medium of various types, scale changes, numerical simulation calculation result, the convergence speed is slow. So the use of computer to this kind of mathematical model for large-scale, fast numerical solution of Paul precision has become the urgent demand in science and engineering. In recent years, there has been a lot of work on the analysis of Darcy-Forchheimer model the Girault and Wheeler value. In the [38] has been proved by nonlinear operator A (V) = mu / sigma beta K-1v+ Monotonicity / P |v|v, mandatory and semi continuity, so as to prove the existence and uniqueness of solutions of Darcy-Forchheimer model, and a suitable inf-sup conditions are given. Then they were considered with piecewise constant and non coordinated Crouzeix-Raviart mixed finite element approximation to the speed and pressure. They proved that the discrete inf-sup condition and mixed yuan format is given the convergence of the Peaceman-Rachford iterative method. At the same time, they use [58] to solve the discrete nonlinear algebraic equations, and proves the convergence of the iterative method. The Peaceman-Rachford iterative method, nonlinear equations and dispersion equation by decoupling, then solving a closed equation of.Lopez, Molina, Salas numerical results of the proposed method in literature [38] in [49], and for Newton and Peaceman-Rachford iterative methods for solving nonlinear equations to do Than. They pointed out that compared with the Peaceman-Rachford iterative method for solving nonlinear equations, Newton method for solving nonlinear equations and no advantage. Because in each iteration, the Newton method requires the solution of a Jacobian matrix, and then solving a linear saddle point system, but in the Peaceman-Rachford iteration, only for nonlinear equations after a decoupling calculation one for the introduction of intermediate values, a linear saddle point problem and solving simplified. Compared with the formation of a Jacobian matrix to work, solving nonlinear equation decoupling after consumption of the workload can be neglected. Moreover, in the selection of initial iterative value under the condition of the same, Peaceman-Rachford iteration than the iterative step of Newton convergence the number is less. The details can be Darcy-Forchheimer model reference [49].Park depends on the time in the literature [56] presented a half from Mixed element format.Pan and Rui powder in [54] of Darcy-Forchheimer model is presented based on Raviart-Thomas (RT) or Brezzi-Douglas-Marini (BDM) element approximation speed, approximation of the mixed finite element method with piecewise constant pressure dual form. They will speed the Darcy-Forchheimer model as a function of pressure gradient, obtained a nonlinear only with monotone pressure elliptic partial differential equations, and the regularity of monotone non Degenerate Equations prove that the continuous and discrete problems based on the conditions of inf-sup, prove the existence and uniqueness of the solution. Finally, the monotonicity of the Darcy-Forchheimer operator to speed L2, L3 norm, L2 norm pressure a priori error estimation of.Rui and Pan in [63] gives the block centered finite difference Darcy-Forchhcimer model method, the block centered finite difference numerical integral formula can be considered under appropriate The lowest order mixed finite element method RT-P0.Rui, Zhao and Pan in [64] Forchheimer for the Darcy-Forchheimer coefficient in the model is variable, namely beta (x), the block center of the finite difference method of.Wang and Rui in [76] of Darcy-Forchheimer model to build a stable Crouzeix-Raviart mixed element the methods of.Rui and Liu in [62] of Darcy-Forchheimer model introduces a double grid block centered finite difference method.Salas, Lopez, and Molina in [67] are given in the analysis of mixed finite element method in the literature they achieve in the [49] theory, and obtain the well posedness analysis and convergence proof. Most of the previous the above mentioned work mainly focuses on the discrete method of Darcy-Forchheimer model. In addition to the Peaceman-Rachford iteration method mentioned in the literature [38], there is little work on exploring needle A fast method for solving nonlinear saddle point problems are scattered, and this is the starting point and the theme of the thesis. The multigrid method is one of the many methods, for solving linear and nonlinear elliptic problems. In particular, for nonlinear problems, we won't get a simple linear residual equation. This is the most important difference between linear and nonlinear problems. Here we use multigrid scheme is the multigrid method we used to solve nonlinear problems, approximate format for (FAS) [20]. because we in solving problems with a coarse grid is not only full approximation error in this paper. The Darcy-Forchheimer porous medium model is constructed for nonlinear multigrid method of coordinated and non coordinated discrete mixed finite element method are given respectively based on the effective. We use the Peaceman-Rachford iteration method The decoupling of nonlinear equation and mass conservation equation for smoother in the multigrid method. We put the saddle point linear problem is simplified into a problem of solving symmetric positive definite, and illustrate the validity of our approach. This is used for splitting parameter equations and constraint conditions of nonlinear decoupling, different values of Forchheimer coefficient the beta [49], always take a = 1, and we found a better value, and that we take the value of better times and CPU by comparison to iterative calculation time. We do a lot of numerical experiments to illustrate the effectiveness of the multigrid solver we construct the convergence. Methods we constructed that does not depend on the mesh size is not dependent on the number of Forchheimer, and our computational complexity is close to linear. It is a reminder that constructing a fast Fast calculation method does not depend on some important parameters is not an easy thing, such as literature [50, treatment for a class of linear Stokes equations in 53]. The paper is organized as follow: the first chapter briefly introduces the Darcy-Forchheimer equation in porous media and its scope of application, and the law of conservation of mass and deformation under various assumptions. The mathematical model of the process, the basic equation is coupled equations. In the second chapter, a brief review of the basic numerical calculation method. The discrete equations are solved including the direct solution of linear equations and linear iterative method and nonlinear iterative method. In addition to the introduction of different numerical methods, also a brief overview of each method is effective applicable. And explain the advantages and disadvantages of the iterative method based on the classical iteration. This matter is to "smooth" function, which can quickly to eliminate the residual The high frequency part in the amount, but the low frequency part, the effect is not very good. The classical iterative method for solving the two-dimensional Poisson problem of homogeneous Dirichlet boundary as an example to illustrate the smooth nature of the iterative method. The third chapter introduces the idea of multigrid method is the most basic and the most basic algorithm. Firstly introduces the linear multigrid because the error of the linear methods, satisfying residual equation, but it is not suitable for nonlinear problems, the nonlinear problems, need to adopt a different strategy. It introduces two kinds of nonlinear multigrid method. In the fourth chapter, the Darcy-Forchheimer porous medium model to construct the coordination discrete mixed finite element method gives an effective based on the nonlinear multigrid method. We use the Peaceman-Rachford iteration as smoothers in the multigrid method to decouple the nonlinear equations and mass conservation equations. The saddle point linear problem is simplified into a problem of solving symmetric positive definite, and we illustrate the effectiveness of this approach. We used for splitting parameter alpha decoupled nonlinear equations and constraint conditions, different values of Forchheimer coefficient in [49], the total is alpha = 1, and we found a better value, and that we take the value of better times and CPU by comparison to iterative calculation time. We do a lot of numerical experiments to illustrate the effectiveness of the multigrid algorithm. We construct the convergence method we construct that does not depend on the mesh size is not dependent on Forchheimer coefficient and, our computational complexity is close to linear. This part from the [42], this article has been in the Journal Journal of Scientific Computing (SCI) published online. In the fifth chapter, the In porous media Darcy-Forchheimer model to construct the nonconforming mixed finite element method discrete gives an efficient nonlinear multigrid method based on nonconforming mixed finite element multigrid and coordination mixed finite element multigrid compared to the most important difference is the discrete space is not nested, so in the conversion between grid function in different grid, we can't get by mapping simple again. The key issue is how to construct the grid between the projection operator. And coordinate multigrid methods, we do a lot of numerical experiments to illustrate the effectiveness of the multigrid algorithm we constructed. I

【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.8;O357.3

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