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Higher-order, strongly stable methods for uncoupling groundwater-surface water flow.

機譯：解耦地下水與地表水流的高階，高度穩(wěn)定方法。

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摘要

Many environmental problems today involve the prediction of the migration of contaminants in groundwater-surface water flow. Sources of contaminated groundwater-surface water flow include: landfill leachate, radioactive waste from underground storage containers, and chemical run-off from pesticide usage in agriculture, to name a few. Before we can track the transport of pollutants in environmental flow, we must first model the flow itself, which takes place in a variety of physical settings. This necessitates the development of accurate numerical models describing coupled fluid (surface water) and porous media (groundwater) flow, which we assume to be described by the fully evolutionary Stokes-Darcy equations. Difficulties include finding methods that converge within a reasonable amount of time, are stable when the physical parameters of the flow are small, and maintain stability and accuracy along the interface. Ideally, because there exist a wide variety of physical scenarios for this coupled flow, we desire numerical methods that are versatile in terms of stability and practical in terms of computational cost and time.;The approach to model this flow studied herein seeks to take advantage of existing efficient solvers for the separate sub-flows by uncoupling the flow so that at each time level we may solve a separate surface and groundwater problem. This approach requires only one (SPD) Stokes and one (SPD) Darcy sub-physics and sub-domain solve per time level for the time-dependent Stokes-Darcy problem. In this dissertation, we investigate several different methods that uncouple groundwater-surface water flow, and provide thorough analysis of the stability and convergence of each method along with numerical experiments.
機譯：今天，許多環(huán)境問題都涉及對地下水-地表水流中污染物遷移的預測。污染的地下水-地表水流的來源包括：垃圾滲濾液，地下存儲容器中的放射性廢物以及農(nóng)業(yè)中使用農(nóng)藥引起的化學徑流等。在跟蹤環(huán)境流中污染物的遷移之前，我們必須首先對流本身進行建模，這是在各種物理環(huán)境中進行的。這需要開發(fā)描述耦合的流體（地表水）和多孔介質(zhì)（地下水）流的精確數(shù)值模型，我們假設(shè)該模型將由完全演化的Stokes-Darcy方程來描述。困難包括尋找在合理的時間內(nèi)收斂，在流動的物理參數(shù)較小時保持穩(wěn)定并在界面上保持穩(wěn)定性和準確性的方法。理想情況下，由于存在這種耦合流的多種物理方案，因此我們希望數(shù)值方法在穩(wěn)定性方面具有通用性，而在計算成本和時間方面則是實用的。通過解耦流來分離流的現(xiàn)有有效求解器，以便在每個時間級別我們都可以解決地表水和地下水的問題。對于與時間有關(guān)的Stokes-Darcy問題，此方法每個時間級別僅需要一個（SPD）Stokes和一個（SPD）Darcy子物理學和子域求解。本文研究了幾種分離地下水-地表水流的方法，并通過數(shù)值實驗對每種方法的穩(wěn)定性和收斂性進行了詳盡的分析。

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  • 作者

    Kubacki, Michaela.;

  • 作者單位

    University of Pittsburgh.;

  • 授予單位 University of Pittsburgh.;
  • 學科 Mathematics.
  • 學位 Ph.D.
  • 年度 2014
  • 頁碼 154 p.
  • 總頁數(shù) 154
  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類
  • 關(guān)鍵詞

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