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Numerical methods for inverse problem of heat conduction with unknown boundary based on variational principles with variable domain

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Abstract

In this article a variable-domain variational approach to the entitled problem is presented. A pair of complementary variational principles with a variable domain in terms of temperature and heat-streamfunction are first established. Based on them, two methods of solution—generalized Ritz method and variable-domain FEM—both capable of handling problems with unknown boundaries, are suggested. Then, three sample numerical examples have been tested. The computational process is quite stable, and the results are encouraging. This variational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems in mathematical physics.

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Authors and Affiliations

  1. Shanghai University of Technology and Shanghai Institute of Appl. Math. & Mechanics, 200072, Shanghai, China

    Liu Gao-Lian (Professor)

  2. Shanghai Institute of Mechanical Engineering, 200093, Shanghai, China

    Zhang Dao-Fang (Research Assistant)

Authors
  1. Liu Gao-Lian
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  2. Zhang Dao-Fang
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Liu, GL., Zhang, DF. Numerical methods for inverse problem of heat conduction with unknown boundary based on variational principles with variable domain. J. of Thermal Science 1, 241–248 (1992). https://doi.org/10.1007/BF02653203

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  • DOI: https://doi.org/10.1007/BF02653203

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