A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem

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A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem. / Sorokin, S. B.

In: Journal of Applied and Industrial Mathematics, Vol. 17, No. 3, 09.2023, p. 651-663.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{bf6f0397ca504861bf407ea8c1791ad8,

title = "A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem",

abstract = "The continuation problem for the heat equation is considered. Determining the heat fluxon an inaccessible boundary reduces to an inverse problem. An implicit difference scheme is usedfor the numerical solution of the inverse problem. At each time step, the heat flux on theinaccessible boundary is calculated for the difference analog of the elliptic equation byan economical direct method. The proposed algorithm substantially expands the range ofproblems being solved and can be used to create devices capable of real-time determination of theheat flux on parts of inhomogeneous structures inaccessible for measurements, for example, on theinner radius of pipes made of various materials.",

keywords = "direct method, discrete analog, heat conduction problem, heat flux, inaccessible boundary, inverse problem, mathematical model, numerical solution",

author = "Sorokin, {S. B.}",

note = "The work was carried out within the framework of the state assignment of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, project no. 0251-2021-0001. Публикация для корректировки.",

year = "2023",

month = sep,

doi = "10.1134/S1990478923030183",

language = "English",

volume = "17",

pages = "651--663",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - A Difference Method for Calculating the Heat Flux on an Inaccessible Boundary in a Heat Conduction Problem

AU - Sorokin, S. B.

N1 - The work was carried out within the framework of the state assignment of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, project no. 0251-2021-0001. Публикация для корректировки.

PY - 2023/9

Y1 - 2023/9

N2 - The continuation problem for the heat equation is considered. Determining the heat fluxon an inaccessible boundary reduces to an inverse problem. An implicit difference scheme is usedfor the numerical solution of the inverse problem. At each time step, the heat flux on theinaccessible boundary is calculated for the difference analog of the elliptic equation byan economical direct method. The proposed algorithm substantially expands the range ofproblems being solved and can be used to create devices capable of real-time determination of theheat flux on parts of inhomogeneous structures inaccessible for measurements, for example, on theinner radius of pipes made of various materials.

AB - The continuation problem for the heat equation is considered. Determining the heat fluxon an inaccessible boundary reduces to an inverse problem. An implicit difference scheme is usedfor the numerical solution of the inverse problem. At each time step, the heat flux on theinaccessible boundary is calculated for the difference analog of the elliptic equation byan economical direct method. The proposed algorithm substantially expands the range ofproblems being solved and can be used to create devices capable of real-time determination of theheat flux on parts of inhomogeneous structures inaccessible for measurements, for example, on theinner radius of pipes made of various materials.

KW - direct method

KW - discrete analog

KW - heat conduction problem

KW - heat flux

KW - inaccessible boundary

KW - inverse problem

KW - mathematical model

KW - numerical solution

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85175850876&origin=inward&txGid=1cc7b5883adfee887c46692705ae6f46

UR - https://www.mendeley.com/catalogue/c58eb8c0-4172-3a77-9bbc-9dc9b365d17d/

U2 - 10.1134/S1990478923030183

DO - 10.1134/S1990478923030183

M3 - Article

VL - 17

SP - 651

EP - 663

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -

ID: 59553841