Cerfacs Enter the world of high performance ...

Numerical Methods



The numerical simulation of physical systems based on partial differential equations plays a central role at CERFACS. Within this transverse axis we study efficient and reliable numerical methods for the numerical approximation and solution of such problems with our partners. We aim at analyzing and developing fast and accurate numerical methods and target a broad range of solution methods adapted to modern parallel platforms.


The main goal is to develop fast and accurate high-order numerical methods for the solution of time-dependent partial differential equations in fluid mechanics related to the simulation of turbulent flows on complex three-dimensional geometries.

Simultaneously, we maintain and further develop expertise on selected core problems in numerical linear algebra that are relevant for both CERFACS teams and shareholders. This includes, e.g., the solution of sparse linear systems of equations with direct, mixed direct/iterative methods or purely iterative methods, the design of preconditioners for Krylov subspace methods exploiting the structure of the system (such as systems of saddle-point type arising in PDE constrained optimization and variational methods in data assimilation), the solution of sequences of linear and nonlinear systems. This research should lead to both new algorithms of interest for the linear algebra community and software available for CERFACS teams and shareholders.

Research fields

  • Aerodynamics
  • Climate modelling
  • Combustion
  • Geophysical flows
  • Structural mechanics



CERFACS Partners

CERFACS Partners


CERFACS Combustion paper on rocket engines selected as Distinguished Paper at the last Int. Symp. on Comb. in Adelaide

superadmin |  14 April 2021

The paper of C. Laurent 'Heat-release dynamics in a doubly- transcritical LO2/LCH4 cryogenic coaxial jet flame subjected to fuel inflow acoustic modulation’  has been selected at the Distinguished Paper in the Gas Turbine and Rocket Engine Combustion colloquium for the 38th International Symposium on Combustion. This paper authored by Laurent, Staffelbach, Nicoud  and  T. Poinsot  is available here:  describes the first LES of a forced doubly transcritical flame.Read more

New Cerfacs’ Activity Report available

superadmin |  25 March 2021

The Cerfacs activity report covering the period from January 2019 to December 2020 is available.Read more