標題: 高度不均勻介質中的橢圓形方程與拋物線方程的數值誤差分析
Numerical Error Analysis for Elliptic and Parabolic Equations in Highly Heterogeneous Media
作者: 葉立明
YEH LI-MING
國立交通大學應用數學系(所)
關鍵字: 非均勻?物線方程式;導數的均勻估計;Non-uniform elliptic equation;uniform gradient estimate
公開日期: 2010
摘要: 這是一個二年期的計劃。我們希望探討計算非均勻橢圓
方程式與非均勻抛物線方程式的方法及這計算方法的誤差
估計問題。以污染源(如化學工廠排放的廢水,核電廠的廢
棄物等) 在地底下的擴散為例。地底下的縫隙結構與地質性
質在不同的位置就有很大的差異,並且污染源擴散時在污染
源的附近或較遠處會有平流與對流現象發生。因此描述此現
象的數學模式就包含了非均勻橢圓方程式與非均勻抛物線
方程式。若是能發展出有效率的計算方法,則可借用計算機
的計算功能幫助我們更清楚了解多孔介質中的多相流在微
觀模式下的細微變化。
之前的計劃大多討論描述多相流的微觀模式與其宏觀
模式之間的關係,也了解一些多相流的微觀模式的均勻收斂
的結果。若是能夠有效率的計算多相流的微觀模式的解。對
多相流在多孔介質中的運動一定能有更進一步的了解。
This is a two-year project. We plan to find efficient numerical
schemes to compute the solutions of non-uniform elliptic equations and
non-uniform parabolic equations. The contaminant transportation and the
multi-phase flows in highly heterogeneous media are strongly related to
the geology of soil and are complicated. Flows in the media may show many
different time-scale phenomenon. Their corresponding microscopic models
usually consist of convection and diffusion equations. In other words,
their mathematical models contain non-uniform elliptic equations and
non-uniform parabolic equations. Therefore, this research helps
understanding waste contaminant transport in soil and flows in porous
media.
In previous projects, we studied models for multi-phase flow problems
in microscopic level and in macroscopic level. We also derive uniform
estimates for solutions of non-uniform elliptic equations. If it is
possible to develop highly efficient numerical schemes to compute the
solutions of non-uniform elliptic equations and non-uniform parabolic
equations, we then have powerful tools to tackle multi-phase flow problem
in porous media.
官方說明文件#: NSC99-2115-M009-009-MY2
URI: http://hdl.handle.net/11536/100083
https://www.grb.gov.tw/search/planDetail?id=2131132&docId=341841
Appears in Collections:Research Plans


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