Nonlinear inverse problem of finding thermophysical characteristics

Abstract

In this paper, a method has been developed for determining the nonlinear heat-conducting characteristics of the soil. Two-layer container complexes were created, the side faces of which are thermally insulated, so the 1D thermal conductivity equation is used. The temperature sensor is placed at the junction of two media, and a mixed boundary value problem is solved in each region. In order to provide the inverse coefficient problem with initial data, two temperature sensors are used: one sensor was placed at the open boundary of the container and recorded the soil temperature at this boundary, and the second sensor was placed a short distance from the boundary, which recorded the air temperature. The measurements were carried out in the time interval (0,4tmax). First, the initial-boundary problem of heat conduction with nonlinear coefficients is studied by the finite difference method. Two types of difference schemes are constructed: linearized and nonlinear. The linearized difference scheme is implemented numerically by the scalar Thomas method, and the nonlinear difference problem is solved by the Newton method. The solution of a linearized difference problem was taken as the initial approximation of Newton’s method. To find the thermophysical parameters, the corresponding functional is minimized using the gradient descent method. In addition, all thermophysical characteristics (8 coefficients) were found for a two-layer container with sand and chernozem.