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Processes 2018, 6(8), 111; https://doi.org/10.3390/pr6080111

A High-Order Numerical Manifold Method for Darcy Flow in Heterogeneous Porous Media

1,2
,
1,* and 1,2
1
Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China
2
College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China
*
Author to whom correspondence should be addressed.
Received: 19 June 2018 / Revised: 27 July 2018 / Accepted: 29 July 2018 / Published: 1 August 2018
(This article belongs to the Special Issue Fluid Flow in Fractured Porous Media)
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Abstract

One major challenge in modeling Darcy flow in heterogeneous porous media is simulating the material interfaces accurately. To overcome this defect, the refraction law is fully introduced into the numerical manifold method (NMM) as an a posteriori condition. To achieve a better accuracy of the Darcy velocity and continuous nodal velocity, a high-order weight function with a continuous nodal gradient is adopted. NMM is an advanced method with two independent cover systems, which can easily solve both continuous and discontinuous problems in a unified form. Moreover, a regular mathematical mesh, independent of the physical domain, is used in the NMM model. Compared to the conforming mesh of other numerical methods, it is more efficient and flexible. A number of numerical examples were simulated by the new NMM model, comparing the results with the original NMM model and the analytical solutions. Thereby, it is proven that the proposed method is accurate, efficient, and robust for modeling Darcy flow in heterogeneous porous media, while the refraction law is satisfied rigorously. View Full-Text
Keywords: Darcy flow; heterogeneity; numerical manifold method; high-order; refraction law Darcy flow; heterogeneity; numerical manifold method; high-order; refraction law
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Zhou, L.; Wang, Y.; Feng, D. A High-Order Numerical Manifold Method for Darcy Flow in Heterogeneous Porous Media. Processes 2018, 6, 111.

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