Coupling radiative, conductive and convective heat-transfers in a single Monte Carlo algorithm: A general theoretical framework for linear situations

It was recently shown that radiation, conduction and convection can be combined within a single Monte Carlo algorithm and that such an algorithm immediately benefits from state-of-the-art computer-graphics advances when dealing with complex geometries. The theoretical foundations that make this coupling possible are fully exposed for the first time, supporting the intuitive pictures of continuous thermal paths that run through the different physics at work. First, the theoretical frameworks of propagators and Green's functions are used to demonstrate that a coupled model involving different physical phenomena can be probabilized. Second, they are extended and made operational using the Feynman-Kac theory and stochastic processes. Finally, the theoretical framework is supported by a new proposal for an approximation of coupled Brownian trajectories compatible with the algorithmic design required by ray-tracing acceleration techniques in highly refined geometry.

Automated summary

It has been shown recently that radiation, conduction, and convection can be combined in a single Monte Carlo algorithm, benefiting from computer-graphics advances for complex geometries. The theoretical foundations for this coupling are fully exposed for the first time, demonstrating continuous thermal paths through different physics. The proposal includes the use of propagators, Green's functions, and Brownian trajectories compatible with ray-tracing acceleration techniques.