| 三维非恒定渗流自由面边界积分项的高精度数值积分 |
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| 引用本文： | 郑桂兰,王媛,裴利华.三维非恒定渗流自由面边界积分项的高精度数值积分[J].水科学进展,2008,19(1):123-128. |
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| 作者姓名： | 郑桂兰 王媛 裴利华 |
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| 作者单位： | 1.河海大学交通学院, 江苏, 南京, 210098; |
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| 基金项目： | 教育部高等学校博士学科点专项科研基金
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国家自然科学基金 |
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| 摘 要： | 在三维非恒定渗流有限元计算中,不可避免地需计算自由面上的边界积分项。建议一种高精度数值积分的方法求取自由面边界积分项。其基本思路是,基于8节点空间等参单元,根据压力为零的边界条件确定自由面满足的曲面方程,将自由面边界积分转化为ξη平面上的二重积分;然后再计算自由面与三维等参单元的交点,将交点投影到局部坐标平面ξη上,并根据点与线的相对关系,确定投影点所围成的局部坐标积分区域;再将总积分区域划分成若干个三角形子区域,并利用变步长Simpson方法计算各三角形子区域上的二重积分,从而实现了高精度的自由面边界积分。该方法避免了单元中自由面为平面的假设,可提高计算精度,特别对于单元内自由面变化剧烈情况,更为显著。将该方法应用于砂槽模型和土坝的渗流分析中,计算结果与实际情况较为接近。
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| 关 键 词： | 非恒定渗流 自由面 数值积分 |
| 文章编号： | 1001-6791（2008）01-0123-06 |
| 收稿时间： | 2007-05-28 |
| 修稿时间： | 2007年5月28日 |
High precision numerical integral on free surface boundary of 3-D unsteady seepage problem |
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| ZHENG Gui-lan,WANG Yuan,PEI Li-hua.High precision numerical integral on free surface boundary of 3-D unsteady seepage problem[J].Advances in Water Science,2008,19(1):123-128. |
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| Authors: | ZHENG Gui-lan WANG Yuan PEI Li-hua |
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| Institution: | 1.College of Traffic and Ocean, Hohai University, Nanjing 210098, China;2.College of Civil Engineering, Hohai University, Nanjing 210098, China |
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| Abstract: | In Getechnical engineering, such as slope, underground tunnel, dam and dike, and soil foundation etc, 3-D unsteady seepage problem often occurs.In performing the numerical analysis of unsteady seepage problem, it is necessary to calculate the integral on free surface boundary.In the paper, a high precision numerical integral method is presented.Based on the 8-node isoparametric element, the equat ion of the free surface boundary in an element is obtained firstly according to zero water pressure condition, and then the integral on the free surface boundary is translated into the integral on the plane ξη of local reference.And the integral region is calculated according to the projections of the intersecting points where free surface and the boundaries of the element cross.Finally the whole integral region is divided into several triangle sub regions, and the Simpson method with changing steps is performed to calculate the integral on each triangle sub-region.The high precision numerical integral method can avoid the assumption that the free surface is a plane within an element.It can improve the calculation accuracy, especially for the case that the free surface within an element varies very sharply The applications in both the sand tank model and an example of homogeneous earth dam are given, it shows that the method is practical. |
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| Keywords: | unsteady seepage free surface numerical integral |
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