本文選題：Green-Ampt入滲模型 + 累積入滲量　； 參考：《水電能源科學(xué)》2017年06期

【摘要】：為解決Green-Ampt(GA)入滲模型只有隱格式解的問題,給出了高精度的顯格式近似解,該顯格式構(gòu)造一組冪函數(shù)作為基函數(shù),通過最小化近似解與精確解之間的誤差,達(dá)到對(duì)GA模型的逼近。在對(duì)誤差函數(shù)最小化的過程中,首先證明優(yōu)化解的存在性,同時(shí)采用自適應(yīng)的優(yōu)化分段方法,在滿足精度的條件下減少基函數(shù)的級(jí)數(shù),達(dá)到簡(jiǎn)化計(jì)算的目的。針對(duì)入滲時(shí)間趨于無窮導(dǎo)致近似解發(fā)散問題,建立了修正公式,確保了該逼近方法的全局收斂性。通過與其他近似解的比較,驗(yàn)證了該方法的穩(wěn)定性和精確性。
[Abstract]:In order to solve the problem that Green-AmptGaA) infiltration model has only implicit scheme solution, a high-precision approximate solution of explicit scheme is given. The explicit scheme constructs a set of power functions as basis functions. By minimizing the error between the approximate solution and the exact solution, the approximation to GA model is achieved. In the process of minimizing the error function, the existence of the optimal solution is first proved. At the same time, the adaptive optimization piecewise method is used to reduce the series of the basis function under the condition of satisfying the accuracy, so as to simplify the calculation. To solve the problem that the infiltration time tends to infinity, a modified formula is established to ensure the global convergence of the approximation method. The stability and accuracy of the method are verified by comparison with other approximate solutions.
【作者單位】： 長(zhǎng)江工程職業(yè)技術(shù)學(xué)院水利工程系;
【分類號(hào)】：S152.7

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