DOI: 10.1002/cnm.1640100504. Addressing the corner problem in BEM solution of heat conduction problems

Addressing the corner problem in BEM solution of heat conduction problems

10.1002/cnm.1640100504

Crossref journal-article

Wiley

Communications in Numerical Methods in Engineering (311)

Abstract

AbstractA numerical problem which features prominently in the implementation of the boundary‐element method (BEM) for the solution of heat‐conduction problems arises from double‐valued heat fluxes at boundary corners. This problem is readily dealt with by explicitly treating nodal heat fluxes as double‐valued prior to assembly of the nodal equations. This formulation is very flexible as it also permits imposing discontinuous thermal conditions at any boundary node. However, at corner nodes where temperature only is prescribed, the scheme leads to two unknowns, while only one nodal BEM equation is available there. An additional equation which closely follows the previous work of Walker and Fenner is derived for these nodes, and this provides sufficient information to resolve the upstream and downstream values of the heat flux at the temperature node. The additional equation is general, is free of heuristic constraints, and is applicable through the wide range of acute, shallow, obtuse and re‐entrant angles encountered in practice. Numerical examples are used to compare the present method with the Walker and Fenner approach and with analytical solutions. Results indicate both improved accuracy and generality, thus validating the present method.

Bibliography

Kassab, A. J., & Nordlund, R. S. (1994). Addressing the corner problem in BEM solution of heat conduction problems. Communications in Numerical Methods in Engineering, 10(5), 385â392. Portico.

Authors 2

Alain J. Kassab (first)
R. S. Nordlund (additional)

References 16 Referenced 9

{'key': 'e_1_2_1_2_2', 'volume-title': 'The Boundary Element Method for Engineers', 'author': 'Brebbia C. A.', 'year': '1978'} / The Boundary Element Method for Engineers by Brebbia C. A. (1978)
{'key': 'e_1_2_1_3_2', 'volume-title': 'Boundary Element Methods in Engineering Science', 'author': 'Banerjee P. K.', 'year': '1981'} / Boundary Element Methods in Engineering Science by Banerjee P. K. (1981)
10.1007/978-3-642-48860-3
10.1098/rspa.1963.0153
10.1002/nme.1620100503
P.Ricardella ‘An implementation of the boundary integral techniques for plane problems in elasticity and elasto‐plasticity ’ Ph.D. thesis Carnegie Mellon University Pittsburgh 1973.
10.1016/0307-904X(77)90046-4
{'key': 'e_1_2_1_9_2', 'volume-title': 'Computational Engineering with Boundary Elements', 'author': 'Detournay C.', 'year': '1990'} / Computational Engineering with Boundary Elements by Detournay C. (1990)
10.1016/0045-7949(79)90105-6
{'key': 'e_1_2_1_11_2', 'first-page': '45', 'volume-title': 'Progress in Boundary Element Methods', 'author': 'Paris F.', 'year': '1989'} / Progress in Boundary Element Methods by Paris F. (1989)
{'key': 'e_1_2_1_12_2', 'first-page': '603', 'volume-title': 'SECTAM XIII Proceedings: The Southeastern Conference on Theoretical and Applied Mechanics', 'author': 'Liu J. C.', 'year': '1986'} / SECTAM XIII Proceedings: The Southeastern Conference on Theoretical and Applied Mechanics by Liu J. C. (1986)
10.1002/nme.1620281107
10.1007/978-1-4899-2877-1_7
10.1002/nme.1620231008
10.1002/nme.1620260103
R. S.Nordlund ‘Application of the boundary element method to steady‐state and transient heat conduction problems’ M.S. thesis University of Florida Gainesville 1992.

Dates

Type	When
Created	20 years ago (Aug. 9, 2005, 3:26 a.m.)
Deposited	1 year, 10 months ago (Oct. 24, 2023, 12:43 p.m.)
Indexed	1 year, 10 months ago (Oct. 26, 2023, 12:56 a.m.)
Issued	31 years, 3 months ago (May 1, 1994)
Published	31 years, 3 months ago (May 1, 1994)
Published Online	20 years, 2 months ago (June 21, 2005)
Published Print	31 years, 3 months ago (May 1, 1994)

Funders 0

None

BibTeX

@article{Kassab_1994, title={Addressing the corner problem in BEM solution of heat conduction problems}, volume={10}, ISSN={1099-0887}, url={http://dx.doi.org/10.1002/cnm.1640100504}, DOI={10.1002/cnm.1640100504}, number={5}, journal={Communications in Numerical Methods in Engineering}, publisher={Wiley}, author={Kassab, Alain J. and Nordlund, R. S.}, year={1994}, month=may, pages={385–392} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2023,
        10,
        26
      ]
    ],
    "date-time": "2023-10-26T04:56:09Z",
    "timestamp": 1698296169587
  },
  "reference-count": 16,
  "publisher": "Wiley",
  "issue": "5",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2005,
            6,
            21
          ]
        ],
        "date-time": "2005-06-21T00:00:00Z",
        "timestamp": 1119312000000
      },
      "content-version": "vor",
      "delay-in-days": 4069,
      "URL": "http://onlinelibrary.wiley.com/termsAndConditions#vor"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1994,
        5
      ]
    ]
  },
  "abstract": "<jats:title>Abstract</jats:title><jats:p>A numerical problem which features prominently in the implementation of the boundary\u2010element method (BEM) for the solution of heat\u2010conduction problems arises from double\u2010valued heat fluxes at boundary corners. This problem is readily dealt with by explicitly treating nodal heat fluxes as double\u2010valued prior to assembly of the nodal equations. This formulation is very flexible as it also permits imposing discontinuous thermal conditions at any boundary node. However, at corner nodes where temperature only is prescribed, the scheme leads to two unknowns, while only one nodal BEM equation is available there. An additional equation which closely follows the previous work of Walker and Fenner is derived for these nodes, and this provides sufficient information to resolve the upstream and downstream values of the heat flux at the temperature node. The additional equation is general, is free of heuristic constraints, and is applicable through the wide range of acute, shallow, obtuse and re\u2010entrant angles encountered in practice. Numerical examples are used to compare the present method with the Walker and Fenner approach and with analytical solutions. Results indicate both improved accuracy and generality, thus validating the present method.</jats:p>",
  "DOI": "10.1002/cnm.1640100504",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        8,
        9
      ]
    ],
    "date-time": "2005-08-09T07:26:17Z",
    "timestamp": 1123572377000
  },
  "page": "385-392",
  "source": "Crossref",
  "is-referenced-by-count": 9,
  "title": "Addressing the corner problem in BEM solution of heat conduction problems",
  "prefix": "10.1002",
  "volume": "10",
  "author": [
    {
      "given": "Alain J.",
      "family": "Kassab",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "R. S.",
      "family": "Nordlund",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "311",
  "published-online": {
    "date-parts": [
      [
        2005,
        6,
        21
      ]
    ]
  },
  "reference": [
    {
      "key": "e_1_2_1_2_2",
      "volume-title": "The Boundary Element Method for Engineers",
      "author": "Brebbia C. A.",
      "year": "1978"
    },
    {
      "key": "e_1_2_1_3_2",
      "volume-title": "Boundary Element Methods in Engineering Science",
      "author": "Banerjee P. K.",
      "year": "1981"
    },
    {
      "key": "e_1_2_1_4_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/978-3-642-48860-3"
    },
    {
      "key": "e_1_2_1_5_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1098/rspa.1963.0153"
    },
    {
      "key": "e_1_2_1_6_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/nme.1620100503"
    },
    {
      "key": "e_1_2_1_7_2",
      "unstructured": "P.Ricardella \u2018An implementation of the boundary integral techniques for plane problems in elasticity and elasto\u2010plasticity \u2019 Ph.D. thesis Carnegie Mellon University Pittsburgh 1973."
    },
    {
      "key": "e_1_2_1_8_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0307-904X(77)90046-4"
    },
    {
      "key": "e_1_2_1_9_2",
      "volume-title": "Computational Engineering with Boundary Elements",
      "author": "Detournay C.",
      "year": "1990"
    },
    {
      "key": "e_1_2_1_10_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0045-7949(79)90105-6"
    },
    {
      "key": "e_1_2_1_11_2",
      "first-page": "45",
      "volume-title": "Progress in Boundary Element Methods",
      "author": "Paris F.",
      "year": "1989"
    },
    {
      "key": "e_1_2_1_12_2",
      "first-page": "603",
      "volume-title": "SECTAM XIII Proceedings: The Southeastern Conference on Theoretical and Applied Mechanics",
      "author": "Liu J. C.",
      "year": "1986"
    },
    {
      "key": "e_1_2_1_13_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/nme.1620281107"
    },
    {
      "key": "e_1_2_1_14_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/978-1-4899-2877-1_7"
    },
    {
      "key": "e_1_2_1_15_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/nme.1620231008"
    },
    {
      "key": "e_1_2_1_16_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1002/nme.1620260103"
    },
    {
      "key": "e_1_2_1_17_2",
      "unstructured": "R. S.Nordlund \u2018Application of the boundary element method to steady\u2010state and transient heat conduction problems\u2019 M.S. thesis University of Florida Gainesville 1992."
    }
  ],
  "container-title": "Communications in Numerical Methods in Engineering",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fcnm.1640100504",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://onlinelibrary.wiley.com/doi/pdf/10.1002/cnm.1640100504",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        10,
        24
      ]
    ],
    "date-time": "2023-10-24T16:43:11Z",
    "timestamp": 1698165791000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://onlinelibrary.wiley.com/doi/10.1002/cnm.1640100504"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1994,
        5
      ]
    ]
  },
  "references-count": 16,
  "journal-issue": {
    "issue": "5",
    "published-print": {
      "date-parts": [
        [
          1994,
          5
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1002/cnm.1640100504"
  ],
  "URL": "http://dx.doi.org/10.1002/cnm.1640100504",
  "relation": {},
  "ISSN": [
    "1069-8299",
    "1099-0887"
  ],
  "subject": [],
  "container-title-short": "Commun. Numer. Meth. Engng.",
  "published": {
    "date-parts": [
      [
        1994,
        5
      ]
    ]
  }
}