Estimation of the heat flux at the surface of ablating materials by using temperature and surface position measurements

In this article, the conjugate gradient method with adjoint problem is applied for the identification of the heat flux at the surface of ablating materials, by assuming no a priori information regarding the functional form of the unknown. Simulated measurements of the position of the ablating surface are used in the inverse analysis, together with simulated temperature measurements. The accuracy of the conjugate gradient method with adjoint problem is examined for functions containing sharp corners, by using different regularization approaches. Three different versions of the conjugate gradient method are compared, as applied to the inverse problem under observation.