ANR-HoCo

"Involution preserving High-order Compact numerical methods in multiple dimensions"

ANR (AAPG2025 JCJC CE40) Project HoCo receiving funding 2026—2029.
PI: Wasiij Barsukow

Résumé:
Les méthodes numériques préservant des involutions reproduisent certaines propriétés des solutions
exactes d'équations aux dérivées partielles (EDP) sur des grilles de longueur de discrétisation finie, ce qui
aboutit à des solutions précises sans qu'il soit nécessaire d'affiner excessivement la grille. Le premier
objectif du projet HoCo est de développer des méthodes numériques compactes d'ordre élevé
véritablement multidimensionnelles pour les lois de conservation qui préservent des involutions dans les
régions d'écoulement lisse tout en étant capables de gérer les discontinuités/chocs. Parvenir à une
compréhension globale de la manière dont cela peut être réalisé à travers les différentes méthodes
compactes d’ordre élevé est son deuxième objectif.

Abstract:
Involution-preserving numerical methods reproduce certain properties of exact solutions of partial
differential equations (PDEs) on grids with finite discretization length, which results in accurate solutions
without the need to excessively refine the grid. The first aim of the HoCo project is to develop truly multi-
dimensional high-order compact numerical methods for conservation laws that are involution-preserving in
regions of smooth flow while being able to handle discontinuities/shocks. To arrive at an overarching
understanding of how this can be done throughout the various high-order compact methods is its second
aim.

Open positions

As part of this project, I will be hiring a PhD student to start around September 2026. Do not hesitate to send me an email (wasilij.barsukow@math.u-bordeaux.fr) if you have questions concerning the topics and the position. I might suggest a short (2-4 weeks) mini-project to get to know you better prior to making a decision. If you intend to formally apply, i.e. whenever you are sending me your CV please also include

• a motivation statement, with info on why you are interested in numerics and in PDEs, how you think you can contribute and whether you are willing to do a mini-project,
  
• a description of your experience in numerical analysis and software development, possibly with references to (public) repositories,
  
• an academic reference (professor, supervisor of master's thesis, etc.) who knows you (email/phone number).
  

I will only consider complete applications. Please note that this step is an inofficial one (being a selection on scientific grounds) and your application will also require official approval on formal and administrative grounds by the doctoral school (e.g. you will need to be in the possession of a relevant diploma, etc.).

The language of the supervision and email communication can be French, English or German; you choose.

Last modified: Wed Aug 06 18:43:43 CEST 2025