Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SEMI-DISCRETE CENTRAL DIFFERENCE METHOD FOR DETERMINING SURFACE HEAT FLUX OF IHCP

  • Qian, Zhi (SCHOOL OF MATHEMATICS AND STATISTICS LANZHOU UNIVERSITY) ;
  • Fu, Chu-Li (SCHOOL OF MATHEMATICS AND STATISTICS LANZHOU UNIVERSITY)
  • Published : 2007.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

We consider an inverse heat conduction problem(IHCP) in a quarter plane which appears in some applied subjects. We want to determine the heat flux on the surface of a body from a measured temperature history at a fixed location inside the body. This is a severely ill-posed problem in the sense that arbitrarily "small" differences in the input temperature data may lead to arbitrarily "large" differences in the surface flux. A semi-discrete central difference scheme in time is employed to deal with the ill posed problem. We obtain some error estimates which also give the information about how to choose the step length in time. Some numerical examples illustrate the effects of the proposed method.

Keywords

References

  1. J. V. Beck, B. Blackwell, and S. R. Clair, Inverse Heat Conduction: Ill-posed problems, John Wiley and Sons, Inc., 1985
  2. A. Carasso, Determining surface temperatures from interior observations, SIAM J. Appl. Math. 42 (1982), no. 3, 558-574 https://doi.org/10.1137/0142040
  3. L. Elden, Numerical solution of the sideways heat equation by difference approximation in time, Inverse Problems 11 (1995), no. 4, 913-923 https://doi.org/10.1088/0266-5611/11/4/017
  4. L. Elden, Solving the sideways heat equation by a `method of lines', J. Heat Trans. ASME 119 (1997), 406-412 https://doi.org/10.1115/1.2824112
  5. C. L. Fu and C. Y. Qiu, Wavelet and error estimation of surface heat flux, J. Comput. Appl. Math. 150 (2003), no. 1, 143-155 https://doi.org/10.1016/S0377-0427(02)00657-X
  6. D. N. Hµao, H.-J. Reinhardt, and A. Schneider, Numerical solution to a sideways para- bolic equation, Internat. J. Numer. Methods Engrg. 50 (2001), no. 5, 1253-1267 https://doi.org/10.1002/1097-0207(20010220)50:5<1253::AID-NME81>3.0.CO;2-6
  7. Z. Qian, C. L. Fu, and X. T. Xiong, Semidiscrete central difference method in time for determining surface temperatures, Int. J. Math. Math. Sci. (2005), no. 3, 393-400 https://doi.org/10.1155/IJMMS.2005.393
  8. X. T. Xiong, C. L. Fu, and H. F. Li, Central difference method of a non-standard inverse heat conduction problem for determining surface heat °ux from interior observations, Appl. Math. Comput. 173 (2006), no. 2, 1265-1287 https://doi.org/10.1016/j.amc.2005.04.070
  9. X. T. Xiong, C. L. Fu, and H. F. Li, Central difference schemes in time and error estimate on a non-standard in- verse heat conduction problem, Appl. Math. Comput. 157 (2004), no. 1, 77-91 https://doi.org/10.1016/j.amc.2003.08.028

Cited by

  1. Lie-group differential algebraic equations method to recover heat source in a Cauchy problem with analytic continuation data vol.78, 2014, https://doi.org/10.1016/j.ijheatmasstransfer.2014.07.010
  2. A quasi-reversibility regularization method for an inverse heat conduction problem without initial data vol.219, pp.23, 2013, https://doi.org/10.1016/j.amc.2013.05.009