Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials
Traditional methods such as the finite difference method, the finite element method, and the finite volume method are all based on continuous interpolation. In general, if discontinuity occurred, the calculation result would show low accuracy and poor stability. In this paper, the numerical manifold...
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MDPI AG
2020-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/10/24/9123 |
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doaj-91e4bd481b55468e9c91249376c324f32020-12-22T00:00:07ZengMDPI AGApplied Sciences2076-34172020-12-01109123912310.3390/app10249123Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre PolynomialsYan Zeng0Hong Zheng1Chunguang Li2State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, ChinaKey Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, ChinaState Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, ChinaTraditional methods such as the finite difference method, the finite element method, and the finite volume method are all based on continuous interpolation. In general, if discontinuity occurred, the calculation result would show low accuracy and poor stability. In this paper, the numerical manifold method is used to capture numerical discontinuities, in a one-dimensional space. It is verified that the high-degree Legendre polynomials can be selected as the local approximation without leading to linear dependency, a notorious “nail” issue in Numerical Manifold Method. A series of numerical tests are carried out to evaluate the performance of the proposed method, suggesting that the accuracy by the numerical manifold method is higher than that by the later finite difference method and finite volume method using the same number of unknowns.https://www.mdpi.com/2076-3417/10/24/9123numerical manifold methoddiscontinuity capturehydrodynamicsadvection equation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yan Zeng Hong Zheng Chunguang Li |
| spellingShingle |
Yan Zeng Hong Zheng Chunguang Li Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials Applied Sciences numerical manifold method discontinuity capture hydrodynamics advection equation |
| author_facet |
Yan Zeng Hong Zheng Chunguang Li |
| author_sort |
Yan Zeng |
| title |
Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials |
| title_short |
Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials |
| title_full |
Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials |
| title_fullStr |
Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials |
| title_full_unstemmed |
Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials |
| title_sort |
discontinuity capture in one-dimensional space using the numerical manifold method with high-order legendre polynomials |
| publisher |
MDPI AG |
| series |
Applied Sciences |
| issn |
2076-3417 |
| publishDate |
2020-12-01 |
| description |
Traditional methods such as the finite difference method, the finite element method, and the finite volume method are all based on continuous interpolation. In general, if discontinuity occurred, the calculation result would show low accuracy and poor stability. In this paper, the numerical manifold method is used to capture numerical discontinuities, in a one-dimensional space. It is verified that the high-degree Legendre polynomials can be selected as the local approximation without leading to linear dependency, a notorious “nail” issue in Numerical Manifold Method. A series of numerical tests are carried out to evaluate the performance of the proposed method, suggesting that the accuracy by the numerical manifold method is higher than that by the later finite difference method and finite volume method using the same number of unknowns. |
| topic |
numerical manifold method discontinuity capture hydrodynamics advection equation |
| url |
https://www.mdpi.com/2076-3417/10/24/9123 |
| work_keys_str_mv |
AT yanzeng discontinuitycaptureinonedimensionalspaceusingthenumericalmanifoldmethodwithhighorderlegendrepolynomials AT hongzheng discontinuitycaptureinonedimensionalspaceusingthenumericalmanifoldmethodwithhighorderlegendrepolynomials AT chunguangli discontinuitycaptureinonedimensionalspaceusingthenumericalmanifoldmethodwithhighorderlegendrepolynomials |
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