Development of a four-node quadrilateral element-based high order numerical manifold method without linear dependency

2021 ◽  
pp. 1-19
Author(s):  
Hasan Ghasemzadeh ◽  
Peyman Mohsenzadeh ◽  
Khosro Shabani
Keyword(s):  
High Order ◽  
Numerical Manifold Method ◽  
Quadrilateral Element ◽  
Linear Dependency ◽  
Numerical Manifold

Investigation of the Accuracy of the Numerical Manifold Method on n-Sided Regular Elements for Crack Problems

2012 ◽  
Vol 157-158 ◽  
pp. 1093-1096
Author(s):  
Hui Hua Zhang ◽  
Jia Xiang Yan
Keyword(s):  
Numerical Manifold Method ◽  
Quadrilateral Element ◽  
Regular Elements ◽  
Linear Elastic ◽  
Quadrilateral Elements ◽  
Crack Problems ◽  
Elastic Crack ◽  
Triangular Elements ◽  
Numerical Manifold ◽  
Better Than

The numerical manifold method (NMM) is a representative among different numerical methods for crack problems. Due to the independence of physical domain and the mathematical cover system, totally regular mathematical elements can be used in the NMM. In the present paper, the NMM is applied to solve 2-D linear elastic crack problems, together with the comparison study on the accuracy of n-sided regular mathematical elements, i.e., the triangular elements (n=3), the quadrilateral elements (n=4) and the hexagonal elements (n=6). Our numerical results show that among different elements, the regular hexagonal element is the best and the quadrilateral element is better than the triangular one.

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

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 111 ◽  
Author(s):  
Lingfeng Zhou ◽  
Yuan Wang ◽  
Di Feng
Keyword(s):  
Porous Media ◽  
Heterogeneous Porous Media ◽  
High Order ◽  
Darcy Flow ◽  
Numerical Manifold Method ◽  
Material Interfaces ◽  
Darcy Velocity ◽  
Cover Systems ◽  
Numerical Manifold ◽  
Discontinuous Problems

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.

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