本文選題：高維問(wèn)題 + 熱流耦合方程　； 參考：《東華理工大學(xué)》2017年碩士論文

【摘要】：熱流耦合問(wèn)題在地?zé)豳Y源開發(fā)利用、放射性廢物處置、天然氣開發(fā)、地下水開采等方面都廣泛存在.本文對(duì)高維熱流耦合模型進(jìn)行分析,推導(dǎo)出方程的離散格式,對(duì)所得離散格式方程組進(jìn)行了數(shù)值分析,對(duì)耦合模型參數(shù)反演問(wèn)題進(jìn)行了數(shù)值求解.本文首先對(duì)幾種熱流耦合模型進(jìn)行分析,詳細(xì)討論了一種熱流耦合模型的控制方程.用差分法對(duì)耦合方程進(jìn)行數(shù)值離散,構(gòu)造該方程的交替方向迭代(ADI)差分格式,并對(duì)該差分格式進(jìn)行了截?cái)嗾`差分析以及穩(wěn)定性分析,得到差分格式解的條件穩(wěn)定性.熱流耦合方程直接離散后得到非線性方程組.由于非線性方程組求解困難,本文先求出穩(wěn)態(tài)滲流方程在離散點(diǎn)處的滲流速度的數(shù)值解,之后代入離散熱傳導(dǎo)方程,將非線性方程組轉(zhuǎn)化為線性方程組.在高維的情況下,空間域與時(shí)間域網(wǎng)格離散,節(jié)點(diǎn)多,從而導(dǎo)致離散方程組的階數(shù)很大.求解線性方程組系數(shù)矩陣階數(shù)會(huì)很大,采用Thomas算法和克勞特方法對(duì)線性方程組進(jìn)行求解分析.為了提高計(jì)算精度,進(jìn)一步采用廣義極小殘余(GMRES)算法求解分析,并探討該算法的收斂性.進(jìn)行了數(shù)值模擬,驗(yàn)證該數(shù)值方法的可行性.本文最后討論了熱流耦合方程參數(shù)反問(wèn)題,給出了二維熱流耦合方程參數(shù)反演的計(jì)算格式,對(duì)參數(shù)反演格式進(jìn)行了分析,并結(jié)合模擬退火算法進(jìn)行反演計(jì)算和數(shù)值模擬.
[Abstract]:Heat flow coupling problem exists widely in geothermal resources exploitation, radioactive waste disposal, natural gas development, groundwater exploitation and so on. In this paper, the coupling model of high dimensional heat flux is analyzed, the discrete scheme of the equation is deduced, the equations of the discrete form are numerically analyzed, and the parameter inversion problem of the coupled model is solved numerically. In this paper, several heat flux coupling models are analyzed, and the governing equations of a heat flux coupled model are discussed in detail. The coupled equations are discretized numerically by the difference method, and the alternating direction iterative ADI difference scheme is constructed. The truncation error and stability analysis of the scheme are carried out, and the conditional stability of the solution of the difference scheme is obtained. The heat flux coupling equation is discretized directly and the nonlinear equations are obtained. Due to the difficulty of solving the nonlinear equations, the numerical solution of the seepage velocity of the steady state seepage equation at the discrete point is obtained first, and then the discrete heat conduction equation is replaced, and the nonlinear equations are transformed into the linear equations. In the case of high dimensional space and time domain grids are discrete and there are many nodes resulting in the large order of discrete equations. The order of coefficient matrix for solving linear equations is very large. The Thomas algorithm and the Crowter method are used to solve the linear equations. In order to improve the calculation accuracy, the generalized minimal residual algorithm (GMRES) is used to solve the problem, and the convergence of the algorithm is discussed. Numerical simulation is carried out to verify the feasibility of the numerical method. In the end, the inverse problem of the parameters of the coupled heat flux equation is discussed, and the calculating format of the parameter inversion of the two-dimensional heat flux coupling equation is given. The inversion scheme of the parameters is analyzed, and the inversion calculation and numerical simulation are carried out in combination with the simulated annealing algorithm.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.8

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本文編號(hào)：1910767