Solution of inverse heat conduction problems with phase changes by the mollification method

Abstract

The mollification method, originally developed for the solution of the inverse heat conduction problem, is implemented as a front-tracking, space marching, finite difference procedure to determine the location of the solid/liquid interface in one-dimensional melting problems. The technique is “reversible” in the sense that if the temperature history is approximately known at two arbitrary points in the liquid region or in the solid region, the Stefan problem is solved by marching forward or backward in space. The method is also applied to the solution of the inverse Stefan problem, where the temperature and heat flux histories are measured at the transient front interface and the temperature and heat flux histories at the fixed boundary are desired. The accuracy of the algorithm is illustrated by several linear and nonlinear examples where exact and noisy data are considered.