Overview of Advanced Numerical Methods Classified by Operation Dimensions
In this article, the progress of frequently used advanced numerical methods is presented. According to the discretisation manner and manipulation dimensionality, these methods can be classified into four categories: volume-, surface-, line-, and point-operations–based methods. The volume-operation–b...
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| Published in | Aerospace research communications Vol. 1 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
17.07.2023
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| Online Access | Get full text |
| ISSN | 2813-6209 2813-6209 |
| DOI | 10.3389/arc.2023.11522 |
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| Abstract | In this article, the progress of frequently used advanced numerical methods is presented. According to the discretisation manner and manipulation dimensionality, these methods can be classified into four categories: volume-, surface-, line-, and point-operations–based methods. The volume-operation–based methods described in this article include the finite element method and element differential method; the surface-operation–based methods consist of the boundary element method and finite volume method; the line-operation–based methods cover the finite difference method and finite line method; and the point-operation–based methods mainly include the mesh free method and free element method. These methods have their own distinctive advantages in some specific disciplines. For example, the finite element method is the dominant method in solid mechanics, the finite volume method is extensively used in fluid mechanics, the boundary element method is more accurate and easier to use than other methods in fracture mechanics and infinite media, the mesh free method is more flexible for simulating varying and distorted geometries, and the newly developed free element and finite line methods are suitable for solving multi-physics coupling problems. This article provides a detailed conceptual description and typical applications of these promising methods, focusing on developments in recent years. |
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| AbstractList | In this article, the progress of frequently used advanced numerical methods is presented. According to the discretisation manner and manipulation dimensionality, these methods can be classified into four categories: volume-, surface-, line-, and point-operations–based methods. The volume-operation–based methods described in this article include the finite element method and element differential method; the surface-operation–based methods consist of the boundary element method and finite volume method; the line-operation–based methods cover the finite difference method and finite line method; and the point-operation–based methods mainly include the mesh free method and free element method. These methods have their own distinctive advantages in some specific disciplines. For example, the finite element method is the dominant method in solid mechanics, the finite volume method is extensively used in fluid mechanics, the boundary element method is more accurate and easier to use than other methods in fracture mechanics and infinite media, the mesh free method is more flexible for simulating varying and distorted geometries, and the newly developed free element and finite line methods are suitable for solving multi-physics coupling problems. This article provides a detailed conceptual description and typical applications of these promising methods, focusing on developments in recent years. |
| Author | Liu, Hua-Yu Jiang, Wei-Wu Lv, Jun Yang, Kai Cui, Miao Gao, Xiao-Wei Xu, Xiang-Bo |
| Author_xml | – sequence: 1 givenname: Xiao-Wei surname: Gao fullname: Gao, Xiao-Wei – sequence: 2 givenname: Wei-Wu surname: Jiang fullname: Jiang, Wei-Wu – sequence: 3 givenname: Xiang-Bo surname: Xu fullname: Xu, Xiang-Bo – sequence: 4 givenname: Hua-Yu surname: Liu fullname: Liu, Hua-Yu – sequence: 5 givenname: Kai surname: Yang fullname: Yang, Kai – sequence: 6 givenname: Jun surname: Lv fullname: Lv, Jun – sequence: 7 givenname: Miao surname: Cui fullname: Cui, Miao |
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| Cites_doi | 10.1016/0045-7949(80)90149-2 10.1002/nme.1620370202 10.1016/j.ijmecsci.2018.12.032 10.1007/s00231-010-0649-8 10.1007/s11012-014-0014-y 10.1080/10407790.2013.751251 10.1016/j.engfracmech.2020.107510 10.1016/j.compstruct.2016.02.076 10.1016/j.enganabound.2014.05.006 10.1016/j.enganabound.2018.11.008 10.1007/BF00363985 10.1080/10407798708552552 10.13675/j.cnki.tjjs.2017.09.012 10.1016/j.cma.2004.10.008 10.1002/nme.5604 10.1016/j.commatsci.2008.04.006 10.1016/j.euromechsol.2023.104939 10.1007/978-3-319-16874-6 10.1002/(SICI)1097-0207(20000520)48:2<267::AID-NME884>3.0.CO;2-Q 10.1016/j.cma.2019.112613 10.1002/nme.4693 10.1016/j.enganabound.2022.04.025 10.1142/S0219876211002812 10.1016/j.compstruct.2022.116461 10.1142/S0219876216300014 10.1016/j.ijheatmasstransfer.2006.01.013 10.1016/S0955-7997(02)00039-5 10.1016/j.compstruc.2019.02.002 10.1016/j.apm.2018.03.023 10.1016/j.camwa.2007.04.018 10.1016/j.padiff.2022.100477 10.1016/j.tws.2013.09.025 10.1002/nme.1620381010 10.1115/1.1431547 10.1007/978-3-662-11273-1_22 10.7498/aps.71.20220833 10.1007/BF00018439 10.1016/j.camwa.2019.05.026 10.1016/0045-7825(86)90097-6 10.1016/j.ijheatmasstransfer.2017.08.039 10.1002/nme.489 10.1080/10407790.2018.1461491 10.1016/j.cma.2013.09.008 10.1115/1.1433478 10.1016/j.cma.2018.06.021 10.1016/j.jcp.2011.03.010 |
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