INTEGRAL METHOD OF BOUNDARY CHARACTERISTICS IN SOLVING THE STEFAN PROBLEM: DIRICHLET CONDITION

The integral method of boundary characteristics is considered as applied to the solution of the Stefan problem with a Dirichlet condition. On the basis of the multiple integration of the heat-conduction equation, a sequence of identical equalities with boundary characteristics in the form of n-fold integrals of the surface temperature has been obtained. It is shown that, in the case where the temperature profi le is defi ned by an exponential polynomial and the Stefan condition is not fulfi lled at a moving interphase boundary, the accuracy of solving the Stefan problem with a Dirichlet condition by the integral method of boundary characteristics is higher by several orders of magnitude than the accuracy of solving this problem by other known approximate methods and that the solutions of the indicated problem with the use of the fourth–sixth degree polynomials on the basis of the integral method of boundary characteristics are exact in essence. This method surpasses the known numerical methods by many orders of magnitude in the accuracy of calculating the position of the interphase boundary and is approximately equal to them in the accuracy of calculating the temperature profi le.
The integral method of boundary characteristics is considered as applied to the solution of the Stefan problem with a Dirichlet condition. On the basis of the multiple integration of the heat-conduction equation, a sequence of identical equalities with boundary characteristics in the form of n-fold integrals of the surface temperature has been obtained. It is shown that, in the case where the temperature profi le is defi ned by an exponential polynomial and the Stefan condition is not fulfi lled at a moving interphase boundary, the accuracy of solving the Stefan problem with a Dirichlet condition by the integral method of boundary characteristics is higher by several orders of magnitude than the accuracy of solving this problem by other known approximate methods and that the solutions of the indicated problem with the use of the fourth–sixth degree polynomials on the basis of the integral method of boundary characteristics are exact in essence. This method surpasses the known numerical methods by many orders of magnitude in the accuracy of calculating the position of the interphase boundary and is approximately equal to them in the accuracy of calculating the temperature profi le.
Author:  V. A. Kot
Keywords:  heat-conduction equation, Stefan problem, Dirichlet condition, moving interphase boundary, approximation, identical equality
Page:  1289