Adaptive methods for modelling of temperature field of laser irradiated plate

Authors

  • Святослав Алексеевич Лукьяненко National Technical University of Ukraine "Kyiv Polytechnic Institute" 6, Polytechnichna st., Kyiv, 03056, Ukraine
  • Ирина Юрьевна Михайлова National Technical University of Ukraine "Kyiv Polytechnic Institute" 6, Polytechnichna st., Kyiv, 03056, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.19099

Keywords:

method for coordinate-splitting, adaptive method of grid construction, balance method

Abstract

The result of computer modeling of the temperature field of the plate arising under the influence of a moving laser beam is considered in the paper. The comparison of the calculation results, obtained due to the application of implicit schemes of the balance method on the non-uniform adaptive grid with the experimental results was made. At the application of both schemes, two methods of interpolation of the function values - the method of Lagrange of the third degree and the Kochanek-Bartels splines were used in the construction of a new grid. The systems of algebraic equations arising in this difference scheme are solved by the modified Gaussian method in the case of linear circuit and Newton's method in the case of nonlinear circuit. The adaptive method, which "condenses" the nodes in areas with large gradient of temperatures and arranges them more sparsely in areas where the temperature varies smoothly, is used for the automatic construction of a variable of the difference grid. This allows to reduce the calculation time and to get a result with a predetermined accuracy.

The results of computer modeling showed that the nonlinear implicit scheme of the balance method, using the Kochanek-Bartels splines gives a more accurate result. We will also note that the nonlinear scheme of the balance method is a bit more time-consuming as compared to the linear as it requires the implementation of iterations of Newton's method.

Author Biographies

Святослав Алексеевич Лукьяненко, National Technical University of Ukraine "Kyiv Polytechnic Institute" 6, Polytechnichna st., Kyiv, 03056

Professor, Head of APPSD sub-Department

Automation of Power Processes and Systems Design sub-Department

Ирина Юрьевна Михайлова, National Technical University of Ukraine "Kyiv Polytechnic Institute" 6, Polytechnichna st., Kyiv, 03056

Post-graduate student

Automation of Power Processes and Systems Design sub-Department

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Published

2013-12-17

How to Cite

Лукьяненко, С. А., & Михайлова, И. Ю. (2013). Adaptive methods for modelling of temperature field of laser irradiated plate. Eastern-European Journal of Enterprise Technologies, 6(5(66), 12–16. https://doi.org/10.15587/1729-4061.2013.19099

Issue

Vol. 6 No. 5(66) (2013): Applied physics

Section

Applied physics

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Copyright (c) 2014 Святослав Алексеевич Лукьяненко, Ирина Юрьевна Михайлова

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