Research Interests
- Theory and numerics of Boltzmann Transport Equation (BTE)
- Convergence analysis and estimators
- Numerical methods for Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs)
- Acceleration methods for numerical schemes
About my research
I am currently investigating the DPN acceleration method applied to the method of the characteristics (MOC) for solving the BTE for neutrons. This research is related to nuclear reactor physics, specifically lattice calculations.
The MOC consists of solving a PDE along characteristic curves. In Fig. (a) a set of straight-line characteristics is represented, for two directions within a domain D. Solving along a characteristic curve reduces the PDE to an ODE, which is useful for several reasons.
When using numerical methods, one often uses a mesh to partition the domain. When it comes to MOC, there is a transition relation for the flux along a characteristic curve t between two adjacent cells of a mesh, which allows a propagation of information (sweep), as illustrated in Fig. (b).
In nuclear reactor physics, the domain of resolution for the BTE is the reactor core which is usually very large. In order to save computational time, numerical calculations are very often divided into two separate steps: the lattice computation and the core computation.
The lattice step is performed on small parts of the domain (pin cell, assemblies of pins) as shown in Fig. (c). The core step is then performed (on the whole core), using the results obtained during the lattice step.
MOC takes place at the lattice step.
Publications
[1]K. Francois-Elie, S. Santandrea, Acceleration of an improved linear scheme for the neutron transport, Conference paper (2024). https://doi.org/10.1051/epjconf/202430202008.