A numerical solution of the linear multidimensional unsteady inverse heat conduction problem with the boundary element method and the singular value decomposition

Abstract

In this paper, we present a new method for solving the general linear multidimensional unsteady inverse heat conduction problem. The direct numerical method is based on the Boundary Element Method formulation. Taking into account future time steps, the ill-conditioned linear system is solved using a procedure based on the Singular Value Decomposition technique which handles both spatial and temporal instabilities. The regularization method is essentially a spectral truncation method with a single hyperparameter. The optimal value of this hyperparameter can be chosen a priori from the knowledge of the data uncertainty. In the second part of this paper, an experiment is described which illustrates an application of the method on a two-dimensional problem. The physical problem consists in identifying the heat flux on a plate exposed to a moving front of hot fluid from temperature measurements collected on the opposite side of the plate. Numerical results obtained are discussed in comparison to direct heat flux measurements. The purpose of this experiment was to cross-check two types of heat flux sensors in real unsteady two-dimensional situations. It is also shown that the method can be applied to real 3D problems.