Journal of Theoretical
and Applied Mechanics

55, 1, pp. 167-175, Warsaw 2017
DOI: 10.15632/jtam-pl.55.1.167

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

Alicja Piasecka-Belkhayat, Anna Korczak
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.
Keywords: lattice Boltzmann method, directed interval arithmetic, sensitivity analysis