Inverse radiation analysis in two-dimensional gray media using the discrete ordinates method with a multidimensional scheme

This work presents an inverse analysis for temperature field estimation in a two-dimensional gray media; it uses a multidimensional spatial scheme and high order angular quadrature in the discrete ordinates method. The participating media system contains absorbing, emitting, isotropic scattering gray medium. The radiative intensities exiting in some points of boundary surfaces, which simulate data of sensing devises, are known. In this work, the Discrete Ordinates Scheme with Infinitely Small Weight (DOS + ISW) is used to calculate data values. The conjugate gradient method is used to solve the inverse radiation problem for determining the temperature field. The inverse problem is formulated as an optimization problem that minimizes the error between the calculated and the simulated measurement of radiation intensity leaving the media that is sensed at one, two or four points at the boundary of the cavity. The numerical results are obtained by considering simulated data with and without noise. Different arrangements of the position of the sensors at the cavity boundary were analyzed. The temperature field has been estimated with accuracy by using LC11 and Tn6 angular quadratures of DOM when four or two sensors were used and the results for four and two sensors are very close. Also, the effects on the estimations of non-uniform distribution of the absorption coefficient (with random errors of 10%) were analyzed.