Stardis: Propagator evaluation for coupled heat transfer in large geometric models

When heat transfer is linear or can be linearized around a given temperature field, a common engineering practice is to evaluate a propagator for each of the energy sources as well as of the initial temperature field (regarded itself as a source) so that the temperature at a given location and at a later time (a probe point) can be expressed as a simple sum of all sources at all previous times, multiplied by the value of the propagator towards the probe. These simple expressions are then immediately usable for all types of optimization, inversion, sensitivity analysis and command control objectives. However, when facing large CAD geometry models or large numbers of spatially distributed sources, evaluating the relevant propagator values with standard deterministic meshed methods can be a quite difficult or computationally expensive numerical task. On the contrary, Monte Carlo is well known for directly addressing these propagator values as well as for handling large geometrical models with ease. Until quite recently, very few Monte Carlo algorithms could be implemented for coupled transient heat transfer. Recent work on Green formulation and stochastic processes have led to the definition of conducto-convecto-radiative paths and they can now be sampled efficiently using advanced computer graphic tools in order to evaluate the temperature at a probe point, whatever the level of geometrical refinement is. The Stardis project holds an implementation of such recent advances, computing how sources propagate towards a probe point in space-time. A remarkable feature is that Stardis output propagation data themselves, which in turn can be repeatedly used for fast estimation over lots of sets of source values. We detail here this feature of the code and provide all the theoretical background required by a thermal scientist facing the need to use and adapt Stardis.