UDC 519.63
IDENTIFICATION OF THE BOUNDARY MODE
IN ONE THERMAL PROBLEM BASED ON
THE SINGLE-PHASE STEFAN MODEL
Abstract. The process of melting a one-dimensional block of ice by heating it from the left border is considered. A one-dimensional Stefan model is proposed for the mathematical description of the melting process. It describes the temperature change in the resulting melt zone with a movable boundary. Within the framework of this model, the task is to identify the heating mode on the border of the block, which ensures the movement of the movable boundary of the melt zone according to a predetermined law. The posed inverse problem for the single-phase Stefan model belongs to the class of inverse boundary-value problems. With the use of the method of front straightening, the problem area with a movable boundary is transformed into a domain with fixed boundaries. A discrete analog of the inverse problem is constructed using the finite-difference method, and a special representation is proposed for the numerical solution of the resultant difference problem. As a result, the difference problem for each discrete value of the time variable splits into two independent second-order difference problems, for which the absolutely stable Thomas method is used, and a linear equation with respect to the approximate value of the heating temperature at the left boundary of the block. Numerical experiments were carried out on the basis of the proposed computational algorithm.
Keywords: heat transfer with phase transformation, ice melting process, movable phase interface, front rectification method, boundary inverse problem, difference method.
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