Application of Distributed Heat Resource Method for Iterative Solution of Retrospective Inverse Stefan Problem
Retrospective inverse Stefan problem is considered to identify initial temperature condition by temperature measurement for final moment of time. The one-dimensional two-phase inverse Stefan problem added with boundary condition of the third was chosen as a model. To solve the problem we used iterative method of approximate solution. The idea of the method is to find solution of inverse problem through consequent solution of a set of direct problems. Two-layer iterative method of minimum residuals is used to accelerate convergence to initial acceleration. The precise review of main approaches for approximate stable solution with reverse time and numerical solution of classical Stefan problem is presented in the article. In the paper Stefan problem is solved with application of heat phase transfer modification, exactly describing the real process of heat release on the phase transfer interface. Through introduction of the distributed heat resource function, upward to the phase being created, the system of three equations in formulating two-phase Stefan problem is concluded in boundary problem for thermal conductivity equation with discontinuous coefficients. It is solved with sweep method in the implicit difference scheme. We suggest two ways for choosing of heat resource functions as a linear function and dimension functions. We have conducted quasi-real experiment to check soundness of calculating algorithm for retrospective inverse Stefan problem. Distributions of initial temperature were obtained in two ways of choosing the heat resource function. Velocities of iterative process convergence were compared with the method of minimum residuals and consistent iterative parameter.