Lagrange's equations for seepage flow in porous media with a mixed Lagrangian-Eulerian description

doi:10.1007/s10409-023-23022-x

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	Lagrange's equations for seepage flow in porous media with a mixed Lagrangian-Eulerian description
	Wang, LiXiang1 ; Li, ShiHai1,2 ; Feng C(冯春)1,2
通讯作者	Li, Shi-Hai(shli@imech.ac.cn) ; Feng, Chun(fengchun@imech.ac.cn)
发表期刊	ACTA MECHANICA SINICA
	2023-11-01
卷号	39 期号:11 页码:18
ISSN	0567-7718
摘要	Most conventional numerical models employ partial differential equations (PDEs) to describe seepage flow problems and use weighted residual and finite difference solution techniques to solve the PDEs. These PDEs are established in view of a spatial point, which mathematically stems from the infinitesimal concept. An alternative approach to such problems is developed. It applies an energy approach, i.e., the Lagrange's equations, to the representation of the seepage flow system, instead of directly resorting to the PDEs. The Lagrange's functional is established on a representative volume element (RVE) by integrating the energy of the RVE. Following a Lagrange formulation, the variation of the functional is conducted with regard to appropriate generalized coordinates. Then the resulting integral equations are considered with the description from the Lagrangian frame into the Eulerian frame for an improved accuracy. Afterwards, the equations are numerically discretized with a cell-centered finite volume method. Finally, two seepage front estimation schemes are presented-one scheme is implemented by local mesh refinement and the other scheme by seepage front movement. The resulting model is a true energy formulation, developed without reference to the partial differential momentum equations. Numerical examples are demonstrated and show that the model generates physically sound results.
关键词	Lagrange's equations Lagrangian-Eulerian model Seepage flow in porous media Cell-centered finite volume method Seepage front
DOI	10.1007/s10409-023-23022-x
收录类别	SCI ; EI ; CSCD
语种	英语
WOS记录号	WOS:001066634500001
关键词[WOS]	DISCRETE HAMILTONS EQUATIONS ; NUMERICAL MANIFOLD METHOD ; FINITE-ELEMENT-METHOD ; FLUID-FLOW ; DEFORMATION ; DYNAMICS ; MODEL
WOS研究方向	Engineering ; Mechanics
WOS类目	Engineering, Mechanical ; Mechanics
资助项目	National Natural Science Foundation of China[12102059] ; National Key Research and Development Program of China[2018YFC1505504]
项目资助者	National Natural Science Foundation of China ; National Key Research and Development Program of China
论文分区	二类
力学所作者排名	1
RpAuthor	Li, Shi-Hai ; Feng, Chun
引用统计	被引频次：2[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/93000
专题	流固耦合系统力学重点实验室
作者单位	1.Chinese Acad Sci, Key Lab Mech Fluid Solid Coupling Syst, Inst Mech, Beijing 100190, Peoples R China; 2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wang, LiXiang,Li, ShiHai,Feng C. Lagrange's equations for seepage flow in porous media with a mixed Lagrangian-Eulerian description[J]. ACTA MECHANICA SINICA,2023,39,11,:18.
APA	Wang, LiXiang,Li, ShiHai,&冯春.(2023).Lagrange's equations for seepage flow in porous media with a mixed Lagrangian-Eulerian description.ACTA MECHANICA SINICA,39(11),18.
MLA	Wang, LiXiang,et al."Lagrange's equations for seepage flow in porous media with a mixed Lagrangian-Eulerian description".ACTA MECHANICA SINICA 39.11(2023):18.

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