A novel space–time meshless method for solving the backward heat conduction problem

•A novel spacetime meshless method for solving the backward heat conduction problem.•Numerical approximation using the Trefftz basis function of the heat equation.•Collocating the boundary points in the spacetime coordinate system in the Trefftz method.•Highly accurate numerical solutions can be obt...

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Vydáno v:International journal of heat and mass transfer Ročník 130; s. 109 - 122
Hlavní autoři: Ku, Cheng-Yu, Liu, Chih-Yu, Yeih, Weichung, Liu, Chein-Shan, Fan, Chia-Ming
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Elsevier Ltd 01.03.2019
Elsevier BV
Témata:
Backward heat conduction problem
Basis functions
Boundary conditions
Boundary value problems
Collocation methods
Conduction heating
Conductive heat transfer
Coordinates
Finite difference method
Finite element method
Heat conductivity
Inverse problem
Inverse problems
Meshless method
Meshless methods
Numerical analysis
Thermodynamics
Time domain analysis
Trefftz method
Trefftz method
Backward heat conduction problem
Meshless method
Inverse problem
ISSN:0017-9310, 1879-2189
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Shrnutí:•A novel spacetime meshless method for solving the backward heat conduction problem.•Numerical approximation using the Trefftz basis function of the heat equation.•Collocating the boundary points in the spacetime coordinate system in the Trefftz method.•Highly accurate numerical solutions can be obtained comparing to that from conventional time-marching scheme.•Boundary data on the inaccessible boundary can be recovered even the partial data on the final time boundary are absent. This paper presents a novel space–time meshless method for solving the backward heat conduction problem (BHCP). A numerical approximation is obtained using the Trefftz basis function of the heat equation. The Trefftz method, which differs from conventional collocation methods based on a set of unstructured points in space, is used in this study to collocate boundary points in the space–time coordinate system such that the initial and boundary conditions can both be treated as boundary conditions on the space–time domain boundary. Because the solution in time on the boundary of the domain is unknown, the BHCP can be transformed into an inverse boundary value problem. The numerical solution is obtained by superpositioning the Trefftz base functions that automatically satisfy the governing equation. The validity of the proposed method is established for several test problems, including the one-dimensional BHCP and two-dimensional BHCP. The accuracy of the proposed method is compared with that of a conventional time-marching scheme based on the finite difference method. The results demonstrate that highly accurate numerical solutions can be obtained and errors may not accumulate over the entire time domain. Moreover, the boundary data on the inaccessible boundary can be recovered even when the partial data on the final time boundary are absent.
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ISSN:0017-9310
1879-2189
DOI:10.1016/j.ijheatmasstransfer.2018.10.083