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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


A researcher of CERFACS guest during the France Culture radio show « La méthode scientifique » this week

superadmin |  20 January 2020

Mélanie Rochoux,  a researcher at Cerfacs working on wildfire spread modeling at the interface between CFD simulations and data science, is invited to the France Culture radio show « La méthode scientifique » next Wednesday to talk about megafires. Who are they? How are they formed? What are their impacts? How science can provide insights? The radio show is on Wednesday, January 22nd at 4:00 pm on the France Culture's channel.Read more

Thierry Poinsot becomes member of the french Academy of Sciences

superadmin |  14 January 2020

Thierry Poinsot was elected at the french Academy of Sciences in december 2019 with 17 other scientists. This is a great recognition for the work done in Toulouse at IMFT (CNRS) and CERFACS over the last thirty years in CFD and in combustion.    Read more