The post-doctoral contract is funded by the Fondation Mathématique Jacques Hadamard
(FMJH) and the Hadamard Mathematics
Labex (LMH,
public grant as part of the Investissement d'avenir project
ANR-11-LABX-0056-LMH)
to work with
IMOSE (Institut pour la
Modélisation et l'Optimisation des Systèmes et des Énergies) created by
C. Chalons and
L. Dumas, which aims at make a link
between companies with needs of simulation and modelisation and researchers.
IMOSE is a meber of then
MSO network
(Modelisation, Simulation, Optimisation) inaugurated on 28th march 2017 in the Henri
Poincaré Institute (IHP).
The current project is a collaboration with OffiSanté
in order to develop a forecast for the propagation of some pathologies. The input data
are available online and some results
can be seen in a video in the website of
IMOSE.
The objective of this PhD thesis is to design a high-order and explicit finite volume
scheme for specific systems of conservations laws with stiff source terms. Those systems
may degenerate into diffusion equations, for instance this behaviour can be observed with
the isentropic Euler model with friction or with the M1 model for radiative transfer. A
general theory is proposed to design a first-order asymptotic preserving scheme to follow
this degeneracy. The scheme is proved to be stable and consistent under a classical
hyperbolic CFL condition in both hyperbolic and diffusive regimes, for any 2D
unstructured mesh. Moreover, the developed scheme also preserves the set of admissible
states in all regimes, which is mandatory to conserve physical solutions in stiff
configurations.
[5] A. Cherouat, H. Borouchaki, F. Blachère, Métrique et maillage - définition et
bases théoriques, Mise en forme des métaux et fonderie (2023),
10.51257/a-v1-m3011,
[4] F. Blachère and H. Borouchaki, Covariance edges matrix of geometric elements, Annals
of Mathematics and Physics (2023),
10.17352/amp.000088,
[3] F. Blachère, C. Chalons, R. Turpault. Very high-order asymptotic-preserving
schemes for hyperbolic systems of conservation laws with parabolic degeneracy on
unstructured meshes, Computers & Mathematics with Applications (2021),
10.1016/j.camwa.2021.02.003
(pdf
or on HAL),
[2] F. Blachère, R. Turpault. An asymptotic-preserving scheme for systems of
conservation laws with source term on 2D unstructured meshes with high-order MOOD
reconstruction, Comput. Methods Appl. Mech. Engrg. (2017),
10.1016/j.cma.2017.01.012
(pdf
or on HAL),
[1] F. Blachère, R. Turpault, An admissibility and asymptotic-preserving scheme for
systems of conservation laws with source term on 2D unstructured meshes, J. Comput.
Phys. (2016),
10.1016/j.jcp.2016.03.045
(pdf
or on HAL).
Technical report
[1] F. Blachère, C. Chalons, L. Dumas, "Météo santé" : Prévision d’épidémies à partir
de ventes de médicaments, UVSQ, Tech. Rep., Jun. 2017.
CAPS-HyDiL: Comparison of Asymptotic Preserving Schemes for the Hyperbolic to Diffusive
Limit
This code is released under the
GPLv3 license
and implements various scheme in order to make comparisons. Computations are done in 1D
with the telegraph equations using schemes that preserve the diffusive limit implied by
the late-time behaviour and/or with stiff source term. Sources are available
here
and results there
.
AdmAP2D: Admissibility and Asymptotic-Preserving finite volume scheme for systems of
conservation laws with source terms on 2D unstructured meshes
The computational code developed during the PhD is available under the
GPLv3 licence following this
link
.
It computes numerical solutions to system
of conservation laws with source term studied during the PhD on 2D unstructured meshes
using the HLL-DLP-AP scheme. This code is part of the project
ANR ACHYLLES
(Asymptotic Capturing for HYperbolic conservation Laws with LargE Source terms)
of reference
ANR-14-CE25-0001.
This software was registered with the APP
under number IDDN.FR.001.520012.000.S.P.2016.000.31235
on december 16, 2016.
2016-2017: 30h of general math for 1st year students at UVSQ,
2013-2016: 64h per year of teaching in numerical analysis and general mathematics for students
from 1st year to 4th year during the three years of the PhD.
Responsibilities
2016-2018: Involved in the organisation of the CANUM 2018,
2014-2016: Member of the board of the doctoral school
STIM.
Web page at the UTT
IdHAL:
florian-blachere
IdRef:
198304501
ORCID:
0000-0001-7591-2707
scanR:
idref198304501
Scopus Author Identifier:
57188634259
theses.fr:
198304501
zbMATH:
blachere.florian
