| 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
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| Corresponding Author | Li, Shi-Hai([email protected]) ; Feng, Chun([email protected]) |
| Source Publication | ACTA MECHANICA SINICA
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| 2023-11-01 | |
| Volume | 39Issue:11Pages:18 |
| ISSN | 0567-7718 |
| Abstract | 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. |
| Keyword | 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 |
| Indexed By | SCI ; EI ; CSCD |
| Language | 英语 |
| WOS ID | WOS:001066634500001 |
| WOS Keyword | DISCRETE HAMILTONS EQUATIONS ; NUMERICAL MANIFOLD METHOD ; FINITE-ELEMENT-METHOD ; FLUID-FLOW ; DEFORMATION ; DYNAMICS ; MODEL |
| WOS Research Area | Engineering ; Mechanics |
| WOS Subject | Engineering, Mechanical ; Mechanics |
| Funding Project | National Natural Science Foundation of China[12102059] ; National Key Research and Development Program of China[2018YFC1505504] |
| Funding Organization | National Natural Science Foundation of China ; National Key Research and Development Program of China |
| Classification | 二类 |
| Ranking | 1 |
| Contributor | Li, Shi-Hai ; Feng, Chun |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/93000 |
| Collection | 流固耦合系统力学重点实验室 |
| Affiliation | 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 |
| Recommended Citation 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.Rp_Au:Li, Shi-Hai, Feng, Chun |
| 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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| File Name/Size | DocType | Version | Access | License | ||
| Jp2023A096.pdf（1409KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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