A New Numerical Method for an Asymptotic Coupled Model of Fractured Media Aquifer System

Wei Liu; Jintao Cui; Zhifeng Wang

doi:10.1007/s10915-019-01112-z

A New Numerical Method for an Asymptotic Coupled Model of Fractured Media Aquifer System

Wei Liu, Jintao Cui, Zhifeng Wang

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

An asymptotic model coupling three-dimensional and two-dimensional equations is considered to demonstrate the flow in fractured media aquifer system in this paper. The flow is governed by Darcy’s law both in fractures and surrounding porous media. A new anisotropic and nonconforming finite element is constructed to solve the three-dimensional Darcy equation. The existence and uniqueness of the coupled solutions are deduced. Optimal error estimates are obtained in L² and H¹ norms. Numerical experiments show the accuracy and efficiency of the presented method. With the same number of nodal points and the same amount of computational costs, the results obtained by using the new element are much better than those by both Q₁ conforming element and Wilson nonconforming element on the same meshes.

Original language	English
Article number	9
Journal	Journal of Scientific Computing
Volume	82
Issue number	1
DOIs	https://doi.org/10.1007/s10915-019-01112-z
Publication status	Published - 8 Jan 2020

Keywords

Asymptotic coupled model
Karst aquifers
Nonconforming finite element
Numerical analysis

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s10915-019-01112-z

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abstract = "An asymptotic model coupling three-dimensional and two-dimensional equations is considered to demonstrate the flow in fractured media aquifer system in this paper. The flow is governed by Darcy{\textquoteright}s law both in fractures and surrounding porous media. A new anisotropic and nonconforming finite element is constructed to solve the three-dimensional Darcy equation. The existence and uniqueness of the coupled solutions are deduced. Optimal error estimates are obtained in L2 and H1 norms. Numerical experiments show the accuracy and efficiency of the presented method. With the same number of nodal points and the same amount of computational costs, the results obtained by using the new element are much better than those by both Q1 conforming element and Wilson nonconforming element on the same meshes.",

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AU - Liu, Wei

AU - Cui, Jintao

AU - Wang, Zhifeng

PY - 2020/1/8

Y1 - 2020/1/8

N2 - An asymptotic model coupling three-dimensional and two-dimensional equations is considered to demonstrate the flow in fractured media aquifer system in this paper. The flow is governed by Darcy’s law both in fractures and surrounding porous media. A new anisotropic and nonconforming finite element is constructed to solve the three-dimensional Darcy equation. The existence and uniqueness of the coupled solutions are deduced. Optimal error estimates are obtained in L2 and H1 norms. Numerical experiments show the accuracy and efficiency of the presented method. With the same number of nodal points and the same amount of computational costs, the results obtained by using the new element are much better than those by both Q1 conforming element and Wilson nonconforming element on the same meshes.

AB - An asymptotic model coupling three-dimensional and two-dimensional equations is considered to demonstrate the flow in fractured media aquifer system in this paper. The flow is governed by Darcy’s law both in fractures and surrounding porous media. A new anisotropic and nonconforming finite element is constructed to solve the three-dimensional Darcy equation. The existence and uniqueness of the coupled solutions are deduced. Optimal error estimates are obtained in L2 and H1 norms. Numerical experiments show the accuracy and efficiency of the presented method. With the same number of nodal points and the same amount of computational costs, the results obtained by using the new element are much better than those by both Q1 conforming element and Wilson nonconforming element on the same meshes.

KW - Asymptotic coupled model

KW - Karst aquifers

KW - Nonconforming finite element

KW - Numerical analysis

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DO - 10.1007/s10915-019-01112-z

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A New Numerical Method for an Asymptotic Coupled Model of Fractured Media Aquifer System

Abstract

Keywords

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