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Laplace Transform Analytic Element Method. A Semi-analytic Solution for Transient Groundwater Flow Simulation

Автор:   Kristopher K.
мягкая обложка
172 страниц
2010 год
Издательство:   Книга по Требованию
2781 руб
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Описание:Each element is derived for the simplest useful case, an impulse response due to a confined, transient, single-aquifer source. This strategy preserves the accuracy and elegance of the AEM while extending the method to transient phenomena. General temporal behavior is achieved using convolution between these impulse and general time functions; convolution allows the spatial and temporal components of an element to be handled independently. The two-dimensional elements derived here include the point, circle, line segment, ellipse, and infinite line, corresponding to polar, elliptical and Cartesian coordinates. The approach taken here utilizes eigenfunction expansion to derive analytic solutions to the modified Helmholtz equation, then back-transforms the LT-AEM results with a numerical inverse Laplace transform algorithm. The Laplace transform analytic element method (LT-AEM), applies the traditionally steady-state analytic element method (AEM) to the Laplace-transformed diffusion equation (Furman and Neuman, 2003). The extension of these elements to include effects due to leaky, unconfined, multi-aquifer, wellbore storage, and inertia is shown for a few simple elements (point and line), with ready extension to other elements.

Orthomol Immun Junior Сила иммунитета на страже Вашего ребенка Orthomol Immun Junior Сила иммунитета на страже Вашего ребенка

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Discourse on the method of rightly conducting the reason, and seeking truth in the sciences

In this, as appears to me, I was successful enough; for, since I endeavored to discover the falsehood or incertitude of the propositions I examined, not by feeble conjectures, but by clear and certain reasonings, I met with nothing so doubtful as not to yield some conclusion of adequate certainty, although this were merely the inference, that the matter in question contained nothing certain. And, just as in pulling down an old house, we usually reserve the ruins to contribute towards the erection, so, in destroying such of my opinions as I judged to be Ill-founded, I made a variety of observations and acquired an amount of experience of which I availed myself in the establishment of more certain. And further, I continued to exercise myself in the method I had prescribed; for, besides taking care in general to conduct all my thoughts according to its rules, I reserved some hours from time to time which I expressly devoted to the employment of the method in the solution of mathematical difficulties, or even in the solution likewise of some questions belonging to other sciences, but which, by my having detached them from such principles of these sciences as were of inadequate certainty, were rendered almost mathematical: the truth of this will be manifest from the numerous examples contained in this volume ...»

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