# Parallel radiative heat exchange solver for analyzing samples from the OSIRIS-REx space exploration mission

**Project reference: **2123

Spacecraft missions and infrared measurements allowed to know that the surface of most asteroids is covered by a layer of unconsolidated granular material called the *Regolith. *A regolith is defined as a layer or mantle of loose, incoherent, rocky material of whatever origin, that nearly forms the surface of the land and rest on coherent bedrock. Such regolith can be observed in the Moon, Venus, Mars and its satellites, but also in smaller satellites and asteroids. It can be said that regoliths are widespread and it is therefore important to study this material. Furthermore the study of regolith is at the intersection between planetary sciences, space exploration and materials science.

This project aims at studying the thermal response of a regolith. Understanding this thermal response is key since most information about small object of our solar system comes from remote measurements of this Regolith material. In this project we will study the thermal cycles induced by radiative heating on these geometrically complex Regolith material. In particular, the mentor of the project is part of the scientific team of the OSIRIS-REx (space mission from NASA) that is currently orbiting the asteroid *Bennu*. Among other scientific tasks, this mission will send back to Earth a sample of the Regolith of *Bennu *that has successfully been recovered last October. Thus the numerical framework developed in this work will be applied to study the data obtained in the OSIRIS-REx mission.

From a computational perspective, the objective is to model complex radiative heat exchanges between arrangements of particles which are representative of a real Regolith. To this end, a finite element mesh of a particle arrangement can be used to compute the visibility between all the particles’ surfaces. Once the view factors between pairs of surface elements are computed, they can be used to assemble and solve the thermal problem. The main difference compared to a classic finite element solver is that the global stiffness matrix contains radiative exchange terms relating nodes which do not have any element in common. This is challenging for a distributed memory parallel implementation because the stencil of the discretization for surface nodes is quite large and the sparsity of the finite element matrix is reduced.

In this context, the main task that will be carried out in this internship project is to implement a parallel finite element solver to simulate radiative heat exchanges within a Regolith. Existing in-house finite element routines will be used to compute the terms of the nonlinear partial differential equations, which will be solved using the PETSc suite.

We seek for candidates with a strong background on computational mechanics using distributed memory numerical approaches.

**Project Mentor:** Daniel Pino Muños

**Project Co-mentor: **Modesar Shakoor

**Site Co-ordinator: **Karim Hasnaoui

**Learning Outcomes:
**The student will discover the huge amount of research that surrounds a space exploration mission such as OSIRIS-REx. From the technical point of view the student will acquire a strong experience on distributed memory parallelism for solving nonlinear convection-diffusion equations with the finite element method.

**Student Prerequisites (compulsory):
**

- Scientific computing
- C programming
- Distributed memory programming using MPI

**Student Prerequisites (desirable):
**

- PETSc suite
- Finite element method

**Training Materials:
**PETSc tutorials, https://www.mcs.anl.gov/petsc/documentation/tutorials/index.html

**Workplan:
**

Week 2: bibliographic study of the physical problem that will be solved and existing scientific computing libraries and tools

Week 3: PETSc training using online tutorials and plan for the parallel implementation of the nonlinear radiative heat transfer equation using PETSc

Week 4-5: parallel implementation of the nonlinear finite element solver using PETSc

Week 6: optimization of the parallel implementation for large numbers of finite elements and CPUs (weak and strong scalability)

Week 7-8: testing, validation for small and large Regoliths and final report

**Final Product Description:
**A parallel finite element solver that allows to simulate radiative heat exchanges on a geometry representative of a real Regolith.

**Adapting the Project: Increasing the Difficulty:
**The existing ray tracing code for computing the view factors used in the nonlinear heat transfer equation, which has a very poor scalability, could be re-designed with a more optimal parallel implementation.

**Adapting the Project: Decreasing the Difficulty:
**Some aspects relevant to weak and/or strong scalability could be disregarded, for instance the assembly and solution of the equations should be done in parallel but not necessarily the input of the finite element mesh and the view factors, and the output of the temperature, etc

**Resources:
**The students have access to the computational cluster available at CEMEF/Mines ParisTech (60.9 TFlops) in order to carry out the development. Additionnaly, access to the Jean Zay cluster at Idris will also be provided (50000 CPU Hours).

**Organisation:
**

MdlS-Maison de la Simulation (CEA/CNRS)

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