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EN
The paper addresses a two-dimensional boundary identification (reconstruction) problem in steady-state heat conduction. Having found the solution to the Laplace equation by superpositioning T-complete functions, the unknown boundary of a plane region is approximated by polynomials of an increasing degree. The provided examples indicate that sufficient accuracy can be obtained with a use of polynomials of a relatively low degree, which allows avoidance of large systems of nonlinear equations. Numerical simulations for assessing the performance of the proposed algorithm show better than 1% accuracy after a few iterations and very low sensitivity to small data errors.
EN
The paper addresses a boundary identification problem in two-dimensional steady-state heat conduction. The proposed approach based on the Trefftz method allows one to reconstruct the unknown part of a regular domain boundary from the given temperature measurements on it, provided that both the temperature and heat flux on the remaining part of the boundary are known. The reconstruction of an unknown boundary is done through successive approximations with a polynomial or a truncated Fourier series. The proposed solution method, whose merit lies in the avoidance of large systems of nonlinear equations, is fast converging, accurate and numerically stable, as demonstrated in the included numerical examples.
EN
The paper discusses 2-D numerical solution of the inverse boundaiy-geometrical thermal problem consisting of an estimation of the boundary conditions and the position of the phase change in continuous casting process. Sińce this location is, generally, unknown and the mathematical description ofthe problem is not complete, the problem cannot be solved without considering thermal measurements (missing information needs to be replaced by measurements). In order to demonstrate the main advantages ofthe developed formulation, continuous casting of alloy of aluminium was considered as numerical example of inverse thermal anałysis. The results obtained were compared with the experiments and results acquired from other authors.
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