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.

The "teapot in a city": A paradigm shift in urban climate modeling.

Urban areas are a high-stake target of climate change mitigation and adaptation measures. To understand, predict, and improve the energy performance of cities, the scientific community develops numerical models that describe how they interact with the atmosphere through heat and moisture exchanges at all scales. In this review, we present recent advances that are at the origin of last decade's revolution in computer graphics, and recent breakthroughs in statistical physics that extend well-established path-integral formulations to nonlinear coupled models. We argue that this rare conjunction of scientific advances in mathematics, physics, computer, and engineering sciences opens promising avenues for urban climate modeling and illustrate this with coupled heat transfer simulations in complex urban geometries under complex atmospheric conditions. We highlight the potential of these approaches beyond urban climate modeling for the necessary appropriation of the issues at the heart of the energy transition by societies.