InterPore2026

Improved modeling of transient heat conduction in voxelized heterogeneous media using the Brownian walkers method

21 May 2026, 15:35

1h 30m

Poster Presentation (MS18) High-temperature heat and mass transfer within porous materials for energy and space (T > 800 °C) Poster

Speaker

Mr Mattéo Roch (CEA, DAM, Le Ripault)

Description

Porous materials such as felts and foams made of refractory ceramics (Al₂O₃, SiO₂, ZrO₂) offer excellent thermal performance for high-temperature applications, including insulation, atmospheric re-entry shields, heat exchangers, and solar absorbers. To predict their thermal behavior, transient heat transfer must be modeled by coupling conduction and radiation across all material constituents. These heterogeneous media also display complex three-dimensional morphologies, which are numerically reconstructed as voxelized structures using X-ray tomography. Due to the fine spatial discretization necessary to accurately capture the microstructural details, deterministic simulation methods require substantial memory. To address this limitation, we propose a fully stochastic framework: heat conduction is simulated using Brownian walkers and coupled with Monte Carlo ray tracing for radiative transfer.
This work focuses on heat conduction in heterogeneous voxelized structures, specifically on the behavior of Brownian walkers at material interfaces between constituents with different thermo-physical properties. In [1], Seyer et al. proposed an interface treatment for Brownian walkers, but its extension to three-dimensional geometries with closely spaced interfaces remains challenging. Two alternative approaches have been proposed by Lejay et al. [2] and Oukili et al. [3], each offering a distinct treatment of walker behavior. Here, we present the two-dimensional extension of both methods, originally formulated in one dimension.
At each time step, the Brownian walker displacement is governed by an Itō–Taylor scheme, depending on the thermal diffusivity of the originating phase. If the walker encounters an interface between two constituents, its final position must be corrected to account for the thermal diffusivity of the new constituent, especially given the very strong thermo-physical property contrast between air and ceramic phases. Therefore, both approaches rely on a transmission probability at the interface, whereby the walker is either transmitted into the adjacent phase or reflected back into the original one. In Lejay’s method, the local Brownian motion of the walker is taken into account to determine when the first interface is reached within the time step. The remaining Brownian motion is then simulated, accounting for possible multiple interface crossings. Oukili’s approach is directly based on the method of images, which provides an analytical expression for the probability that a walker reaches a given position. Both approaches are first validated in one dimension and then extended to two-dimensional voxelized representations of porous ceramics exhibiting strong thermo-physical property contrasts. Their comparative assessment identifies the most suitable strategy for future fully coupled three-dimensional transient conduction-radiation simulations.