A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains

Wang, Yuan; Hu, Mengsu; Zhou, Quanlin; Rutqvist, Jonny

doi:10.1016/j.apm.2015.08.002

Title: A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains

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Abstract

Numerical manifold method (NMM) is a numerical method known for analyzing continuous and discontinuous mechanical processes in a unified mathematical form. Here in this study we developed a new second-order NMM model to solve the nonlinear problem of water flow with the free surface priori unknown and the difficulty of modeling drains which could dramatically increase the meshing load. Our study consist of: (1) deriving two forms of NMM second-order approximation; (2) constructing the total potential energy for water flow by our energy-work seepage model considering Dirichlet, Neumann and material boundaries uniformly; (3) locating free surface nodes in two forms of second-order approximation; (4) tracking the free surface with an efficient iteration scheme without re-meshing; (5) deriving velocity and tunnel flux by second-order approximation. We developed a new code and demonstrate our model and code with examples including confined drainage tunnel and free surface flow through a dam. We compare the results such as tunnel flux or free surface with linear NMM, analytical or other available numerical solutions. We prove that: the two forms of second-order NMM (1) yield consistent results; (2) for modeling drains involving local intensive change, could achieve accurate result of tunnel flux calculation and dramatically savemore »« less

Authors:

Wang, Yuan;

; Zhou, Quanlin; Rutqvist, Jonny

Publication Date:: Fri Jan 01 00:00:00 EST 2016

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Fossil Energy (FE); National Natural Science Foundation of China (NSFC); Education Ministry Foundation of China; Fundamental Research Funds for the Central Universities; China Scholarship Council

OSTI Identifier:: 1591644

Alternate Identifier(s):: OSTI ID: 1406382; OSTI ID: 1474914

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Published Article

Journal Name:: Applied Mathematical Modelling

Additional Journal Information:: Journal Name: Applied Mathematical Modelling Journal Volume: 40 Journal Issue: 2; Journal ID: ISSN 0307-904X

Publisher:: Elsevier

Country of Publication:: United Kingdom

Language:: English

Subject:: 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; numerical manifold method; second-order; free surface flow; inner drain; fixed mesh; flux calculation

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                    Wang, Yuan, Hu, Mengsu, Zhou, Quanlin, and Rutqvist, Jonny. A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains.  United Kingdom: N. p., 2016. 
Web.  doi:10.1016/j.apm.2015.08.002.

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                    Wang, Yuan, Hu, Mengsu, Zhou, Quanlin, & Rutqvist, Jonny. A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains.  United Kingdom.  https://doi.org/10.1016/j.apm.2015.08.002

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                    Wang, Yuan, Hu, Mengsu, Zhou, Quanlin, and Rutqvist, Jonny. Fri .  
"A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains".  United Kingdom.  https://doi.org/10.1016/j.apm.2015.08.002.

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@article{osti_1591644,

  title        = {A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains},

  author       = {Wang, Yuan and Hu, Mengsu and Zhou, Quanlin and Rutqvist, Jonny},

  abstractNote = {Numerical manifold method (NMM) is a numerical method known for analyzing continuous and discontinuous mechanical processes in a unified mathematical form. Here in this study we developed a new second-order NMM model to solve the nonlinear problem of water flow with the free surface priori unknown and the difficulty of modeling drains which could dramatically increase the meshing load. Our study consist of: (1) deriving two forms of NMM second-order approximation; (2) constructing the total potential energy for water flow by our energy-work seepage model considering Dirichlet, Neumann and material boundaries uniformly; (3) locating free surface nodes in two forms of second-order approximation; (4) tracking the free surface with an efficient iteration scheme without re-meshing; (5) deriving velocity and tunnel flux by second-order approximation. We developed a new code and demonstrate our model and code with examples including confined drainage tunnel and free surface flow through a dam. We compare the results such as tunnel flux or free surface with linear NMM, analytical or other available numerical solutions. We prove that: the two forms of second-order NMM (1) yield consistent results; (2) for modeling drains involving local intensive change, could achieve accurate result of tunnel flux calculation and dramatically save computation load with linear velocity distribution in coarse mesh; (3) for free surface iteration, are efficient with fast convergence to accurate results and with rather coarse mesh. Lastly, as a result, our second-order NMM model is applicable to free surface flow with inner drains for free surface locating and flux calculation, and seepage stability analysis, laying a solid foundation for extending to coupled hydro-mechanical analysis.},

  doi          = {10.1016/j.apm.2015.08.002},

  journal      = {Applied Mathematical Modelling},

  number       = 2,

  volume       = 40,

  place        = {United Kingdom},

  year         = {Fri Jan 01 00:00:00 EST 2016},

  month        = {Fri Jan 01 00:00:00 EST 2016}

}

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