Laboratory of Renewable Energy Science and Engineering

Numerical simulation of coupled conduction-radiation heat transfer through highly porous media in extreme environments

Parallelizing the Radiative Transfer Equation solver

Scientific relevance

Porous materials are used in a wide range of applications involving extreme environments such as solar engineering, high temperature ovens, or space applications, in particular for thermal protection systems for atmospheric (re)entry. To study the thermal response of these types of materials, different phenomena have to be accounted for: conduction, gas convection, potentially chemistry, and internal radiation due to the high levels of temperature inside the porous medium. Conduction and radiation are most of the time coupled by considering a so-called effective conductivity, that groups conduction and radiation within the same heat transfer mechanism.

The goal of this project is to uncouple these two phenomena, by solving the radiative transfer equation (RTE) separately. To do so, a ray tracing Monte-Carlo method is used, which becomes computationally expensive, especially for a standard workstation.

This work has been done by PhD student Jeremy Mora-Monteros as a member of both the LRESE, under the direction of Professor Sophia Haussener, and the former Interdisciplinary Aerodynamics Group led by Dr Pénélope Leyland.

Technical aspects

The radiation code was clearly the bottleneck of the coupled calculation and it was therefore parallelised in MPI, thanks to the help of Vincent Keller, and using the concepts that were taught during the Parallel and High Performance Computing course. The main difficulty was to perform MPI reduce operations on a vector, element to element. For this, a custom MPI operator was created using MPI_op_create.


The speedup achieved with this implementation is almost linear, which could be expected with the implementation of this Monte-Carlo method, as the only communication is done at the time of the reduce operation. Coupled simulations can now be done with a much shorter calculation time, which allows to do parametric studies necessary to verify the code.

This experience is one example of all the support that our group – Interdisciplinary Aerodynamics Group – has received over the last 4 years, especially from Vincent Keller.

Figure 1: Comparison of the divergence of radiative flux inside a porous medium with thickness 1mm, considering black body surfaces at the boundaries

Used software

The HPC clusters at SCITAS use the Slurm workload manager in order to dispatch jobs.

In this work, the Monte-Carlo ray-tracing algorithm is implemented in a home-made Fortran 90 code called MCRAD.

This algorithm is coupled with PAM, an energy equation solver which is part of the PATO toolbox (courtesy of NASA).

The home-made coupling script, called PAMRAC, is written in Python.