Post-Doctoral Research Visit F/M Structure preserving and multidimensional well balanced discretizations for conservation laws

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Type de contrat : Fixed-term contract

Contrat renouvelable : Oui

Niveau de diplôme exigé : PhD or equivalent

Fonction : Post-Doctoral Research Visit

A propos du centre ou de la direction fonctionnelle

The Inria center at the University of Bordeaux is one of the nine Inria centers in France and has about twenty research teams.. The Inria centre is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative SMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute...

Contexte et atouts du poste

This project takes place within ongoing collaborations between the Inria CARDAMOM team, the math department at University of Bordeaux (W. Basukow),  SISSA In Italy (D. Torlo), TU Clausthal in Germany (P. Oeffner), Vellore  Institute of Technology in India (Y Mantri),  and University of Malaga in Spain (C. Parés).

The recruted person will be working in the CARDAMOM inria team in Bordeaux with strong interactions and exchanges with the mentioned collaborators. 

Mission confiée

Context

This project follows the line of long term reserach on the development of improved discretizations for complex PDEs. Here the main focus are hyperbolic balance laws arising in many applications in physics and engineering. More particularly this project looks at so called structure preserving methods which  embed genuinely discrete analogs of continuous constraints. Examples   are  solenoidal constraints and curl involutions, which also include he  enhanced preservation of steady states, often referred to as well balanced. Other constraints as non-negativity or bounded variation  within physically admissible values are also of great importance.

This work follows initial activities on the so called global flux quadrature (GFQ) approach, which has been shown to provide great enhancements in the approximation of stationary states, including multiD solenoidal constraints (see e.g. [GFQ-preprint] to appear on J.Comput.Phys., or [GFQ-talk] presented at the Workshop on numerical approximation of hyperbolic PDEs in honor of Prof. Carlos Parés’ 60th birthday )

The postdoc will contribute to the investigation of several possible extensions of the approach, going from its application to more complex PDE systems, to the methodological enhancements discussed below.

 

Principales activités

Specifically, we aim in the coming years to develop the following aspects

  • applications of the GFQ approach to nonlinear complex multidimensional systems (Shallow Water equations, Euler equations with gravity,  Maxwell equations, MHD, etc)
  • development of subcell limiting strategies compatible with GFQ
  • use of the GFQ strategy to enhance the solution of unsteady problems : space time formulations and ADER
  • combination of GFQ with different numerical techniques: continuous and discontinuous finite elements, finite differences, finite volumes
  • Entropy conservative/stable formulations

The relations with other techniques as e.g. dimension by dimension extensions of the correction method using local solutions of  1D Cauchy problem proposed in [CP20] will also be investigated, as well as their coupling with high order embedded boundary techniques, somewhat in the spirit of [C23,S18].

 

 

Compétences

Technical skills and level required : 

The candidate must have a strong background in the development and implementation of  high order methods for hyperbolic PDES (finite volume and/or difference and/or finite element and/or discontinuous Galerkin).  High proficiency in programming (C, C++, Fortran or Python) is also a must. 

Languages :

English at good working level. 

Relational skills :

The candidte must be able to work in an international environement involving multiple collaborators, and  be willing to travel.

 

Avantages

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of partial teleworking and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Rémunération

gross monthly salary : 2788€ (before social security charges and income tax deduction)