Reconstruction of dynamically changing boundary of multilayer heat conduction composite walls

This paper presents an inverse reconstruction procedure to determine the inner boundary location of heat conduction composite walls from the measurement data of temperature and heat flux on the exterior boundary. Our procedure uses a meshless forward solver that was developed for solving inhomogeneous heat transfer problems across a multilayer composite wall with Cauchy conditions. The forward solver uses the radial basis functions (RBFs) approximation in both time and space in a unified fashion, and hence is well suited for inverse problems. In this work, we consider that the length of the inner layer of the composite wall may vary caused by the material erosion at very high temperature such as in iron-making blast furnaces. In order to mitigate the ill-posed inverse problem, we use the Tikhonov regularization technique to obtain a stable and accurate numerical approximation of the moving boundary. Numerical experiments for a number of examples are presented to demonstrate the effectiveness of our inverse procedure. It can be observed that the error of the inverse solution is smaller or at the same level of noises in the simulated measurement data, demonstrating that our inverse procedure is effective and stable with respect to noisy data for moving boundary problems.