Modeling of thermal processes proceeding in 1D domain of crystalline solids using the lattice Boltzmann method with interval source function

Abstract

The interval lattice Boltzmann method (ILBM) with an uncertainly defined internal heat source function is used to simulate heat transfer in a thin silicone film. The solution to the interval Boltzmann transport equations has been obtained taking into account the rules of directed interval arithmetics. A similar analysis has been done using the sensitivity model where the Boltzmann transport equations and boundary-initial conditions have been differentiated with respect to the no-interval heat source value. The knowledge of the sensitivity function distribution and the application of the Taylor formula allow one to find the border solutions of the problem analyzed, which (to some extent) correspond to the solution obtained under the assumption of the uncertainly defined source function. In the final part of the paper, numerical computations obtained for both methods are presented.