基于子域积分的调整渗透系数法改进
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摘要
调整渗透系数法求解有自由面渗流问题时,数值积分点的布置与自由面的位置无关,自由面穿越单元的渗透矩阵计算容易出现较大的积分误差,导致积分不精确或算法不稳定等。为提高单元渗透矩阵的计算精度,将子域积分引入到无压渗流有限元分析中,对调整渗透系数法进行改进。改进后的方法根据自由面与单元的相交情况将单元划分为若干个子域,然后在每个子域布置数值积分点,可实现对单元渗透矩阵的更准确计算。数值算例计算结果表明:改进后的算法稳定性和收敛性较好。
When the adjusting permeability method is adopted in the analysis of unconfined seepage problem,the layout of the numerical integration points are independent on the location of free surface.Large integration error of the permeability matrix may be generated in the elements that are crossed by the free surface,inducing inaccurate integration or instability.To improve the precision of the permeability matrix,sub-domain integration was introduced in unconfined seepage to improve the adjusting permeability method.In this improved method,elements crossed by free surface were divided into sub-domains according to the position of the free surface and then numerical integration points were sampled in each sub-domain as used to be.By this means,permeability matrix was calculated more precisely.The numerical results show that satisfactory stability and convergence rate have been achieved in the improved algorithm.
When the adjusting permeability method is adopted in the analysis of unconfined seepage problem,the layout of the numerical integration points are independent on the location of free surface.Large integration error of the permeability matrix may be generated in the elements that are crossed by the free surface,inducing inaccurate integration or instability.To improve the precision of the permeability matrix,sub-domain integration was introduced in unconfined seepage to improve the adjusting permeability method.In this improved method,elements crossed by free surface were divided into sub-domains according to the position of the free surface and then numerical integration points were sampled in each sub-domain as used to be.By this means,permeability matrix was calculated more precisely.The numerical results show that satisfactory stability and convergence rate have been achieved in the improved algorithm.
引文
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[7]李新强.无压渗流有限元分析的改进初流量法[J].水利学报,2007,38(8):961-965.
[8]潘树来,王全凤,缙俞.利用初流量法分析有自由面渗流问题之改进[J].岩土工程学报,2012,34(2):202-209.
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[20]邓建霞.有自由面渗流分析的加密高斯点单元传导矩阵调整法[D]:成都:四川大学,2004.
[21]舒仲英,邓建霞,李龙国.加密高斯点单元传导矩阵调整法在有自由面渗流分析中的应用[J].四川大学学报:工程科学版,2007(1):48-52.
[22]介玉新.引用Monte Carlo法的自由面渗流分析[J].清华大学学报:自然科学版,2009(12):1944-1947.
[23]速宝玉,沈振中,赵坚.用变分不等式理论求解渗流问题的截止负压法[J].水利学报,1991(3):22-29.
[24]张乾飞,吴中如.有自由面非稳定渗流分析的改进截止负压法[J].岩土工程学报,2005(1):48-54.
[25]凌道盛.有自由面渗流分析的虚节点法[J].浙江大学学报:工学版,2002,36(3):243-246.
[26]吴梦喜,张学琴.有自由面渗流分析的虚单元法[J].水利学报,1994(8):67-71.
[27]彭华,曹定胜,王家荣,等.有自由面渗流分析的弃单元法及其应用[J].人民长江,1997,28(8):38-40.
[28]梁业国,熊文林.有自由面渗流分析的子单元法[J].水利学报,1997(8):34-38.
[29]彭华,罗谷怀.有自由面渗流分析的子单元法及其应用[J].水电站设计,1996,12(4):24-27.
[30]MoEs N,Dolbow J,Belytschko T.A Finite Element Method for Crack GrowthWithout Remeshing[J].International Journal for Numerical Methods in Engi-neering,1999,46(1):131-150.
[31]Sukumar N,Chopp D L,Mo¨es N,et al.Modeling Holes and Inclusions by Lev-el Sets in the Extended Finite-Element Method[J].Computer Methods in Ap-plied Mechanics and Engineering,2001,190(46-47):6183-6200.
[2]Finn W D L.Finite Element Analysis of Seepage Through Dams[J].Jour-nal of Soil Mechanics&Foundations Division,1972,93(6):41-48.
[3]张有天,陈平,王镭.有自由面渗流分析的初流量法[J].水利学报,1988(8):18-26.
[4]Neuman S P.Saturated-Unsaturated Seepage[J].J Hydraul Div,Am SocCiv Eng,1973,99(12):2233-2250.
[5]Desai C S.Finite Element Residual Schemes for Unconfined Flow[J].Inter-national Journal for Numerical Methods in Engineering,1976,10(6):1415-1418.
[6]王媛.求解有自由面渗流问题的初流量法的改进[J].水利学报,1998(3):68-74.
[7]李新强.无压渗流有限元分析的改进初流量法[J].水利学报,2007,38(8):961-965.
[8]潘树来,王全凤,缙俞.利用初流量法分析有自由面渗流问题之改进[J].岩土工程学报,2012,34(2):202-209.
[9]速宝玉,朱岳明.不变网格确定渗流自由面的节点虚流量法[J].河海大学学报,1991(5):113-117.
[10]杨旭.节点虚流量法的渗流场数值计算与工程应用[D]:广州:中山大学,2005.
[11]崔皓东,朱岳明.有自由面渗流分析的改进节点虚流量全域迭代法[J].武汉理工大学学报:交通科学与工程版,2009(2):238-241.
[12]Baiocchi C,Comincioli V,Magenes E,et al.Free Boundary Problems in theTheory of Fluid Flow Through Porous Media:Existence and Uniqueness Theo-rems[J].Annali Di Matematica Pura Ed Applicata,1973(1):1-82.
[13]Oden J T,Kikuchi N.Theory of Variational Inequalities with Applications toProblems of Flow Through Porous Media[M].Texas:Texas Institute for Com-putational Mechanics,1980.
[14]Bruch J C.Asurvey of Free Boundary Value Problems in the Theory of FluidflowThrough Porousmedia:Variational Inequality Approach[J].Advances in WaterResources,1980,3(2):65-80.
[15]Lacy S J,Prevost J H.Flow Through Porous Media:a Procedure for Locatingthe Free Surface[J].International Journal for Numerical and Analytical Methodsin Geomechanics,1987,11(6):585-601.
[16]Bathe K J,Khoshgoftaar M R.Finite Element Free Surface Seepage AnalysisWithout Mesh Iteration[J].International Journal for Numerical and AnalyticalMethods in Geomechanics,1979,3(1):13-22.
[17]李春华.稳定渗流有限元计算时采用固定网格法的初步研究[G]∥第三届全国渗流力学学术讨论会论文汇编(3).武汉:长江科学院,1986.
[18]王贤能,黄润秋.有自然面渗流分析的高斯点法[J].水文地质工程,1997,24(6):1-4.
[19]周创兵,熊文林,梁业国.求解无压渗流场的一种新方法[J].水动力学研究与进展,1996,11(5):528-534.
[20]邓建霞.有自由面渗流分析的加密高斯点单元传导矩阵调整法[D]:成都:四川大学,2004.
[21]舒仲英,邓建霞,李龙国.加密高斯点单元传导矩阵调整法在有自由面渗流分析中的应用[J].四川大学学报:工程科学版,2007(1):48-52.
[22]介玉新.引用Monte Carlo法的自由面渗流分析[J].清华大学学报:自然科学版,2009(12):1944-1947.
[23]速宝玉,沈振中,赵坚.用变分不等式理论求解渗流问题的截止负压法[J].水利学报,1991(3):22-29.
[24]张乾飞,吴中如.有自由面非稳定渗流分析的改进截止负压法[J].岩土工程学报,2005(1):48-54.
[25]凌道盛.有自由面渗流分析的虚节点法[J].浙江大学学报:工学版,2002,36(3):243-246.
[26]吴梦喜,张学琴.有自由面渗流分析的虚单元法[J].水利学报,1994(8):67-71.
[27]彭华,曹定胜,王家荣,等.有自由面渗流分析的弃单元法及其应用[J].人民长江,1997,28(8):38-40.
[28]梁业国,熊文林.有自由面渗流分析的子单元法[J].水利学报,1997(8):34-38.
[29]彭华,罗谷怀.有自由面渗流分析的子单元法及其应用[J].水电站设计,1996,12(4):24-27.
[30]MoEs N,Dolbow J,Belytschko T.A Finite Element Method for Crack GrowthWithout Remeshing[J].International Journal for Numerical Methods in Engi-neering,1999,46(1):131-150.
[31]Sukumar N,Chopp D L,Mo¨es N,et al.Modeling Holes and Inclusions by Lev-el Sets in the Extended Finite-Element Method[J].Computer Methods in Ap-plied Mechanics and Engineering,2001,190(46-47):6183-6200.