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Shape optimization for a seepage problem with low contrast core

机译：低对比度岩心的渗流问题的形状优化

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In this work we propose a numerical method to minimize the steady flow in the outlet of an embankment dam by optimizing the location of a less permeable material, which is available in a limited amount, inside a matrix of a more permeable material. This is performed by considering the Darcy equation with the permeability taking two different values and a fully saturated media below the phreatic surface. The optimization method is based on an asymptotic relaxation under the assumption of a small contrast between the permeabilities of both materials. Numerical results show the gains obtained when compared to simple layouts for two different volumes of core material and for different contrasts in permeability. Compared to simple layouts and with a core permeability equal to 30% of the permeability of the matrix, the optimized layout reduces the outflow by 15% when compared to putting all the core on the exit side of the dam and by 45% when compared to putting the core as a column in the center of the dam.
机译：在这项工作中，我们提出了一种数值方法，通过优化渗透性较弱的材料基质内部的渗透性较弱的材料（其数量有限）的位置，来最小化路堤坝出口的稳定流量。这是通过考虑达西方程来实现的，该方程的渗透率取两个不同的值，并在潜水面以下完全饱和的介质中。优化方法是基于两种材料的渗透率之间的较小对比的假设下的渐近松弛。数值结果表明，与简单布局相比，两种不同体积的岩心材料以及渗透率的不同对比所获得的收益。与简单布局相比，芯部渗透率等于基体渗透率的30％，与将所有芯部放置在坝的出口侧相比，优化的布局将流出减少了15％，与将核心作为圆柱放在大坝的中心。

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