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Partial Differential Equations

Solving PDEs (partial differential equations) is one of the most important fundamental tasks for solving physics and engineering problems. Efficient numerical algorithms for existing and future computer architectures are one of the main targets. CERFACS performs research on the mathematical fundamentals and on application cases that are of specific interest for CERFACS shareholders, and for which the methods are developed and tested.

Research and progress in PDE methods is deeply rooted in functional analysis, but often the usefulness in practice will depend on the availability of an efficient implementation, and, in particular, the interface to numerical solvers from linear algebra, both direct and iterative. In some applications, unconventional methods, such as mesh-free and kinetic methods (such as the lattice Boltzmann method, LBM) and semistructured mesh methods combined with matrix-free techniques have shown superior potential for high performance computing. In terms of the resolution achieved and the efficiency of execution, we have demonstrated that such methods can outperform conventional techniques by several orders of magnitude. This gain in efficiency promises enormous savings  or, equivalently, a superior fidelity and improved predictive power of the simulations.

A – Legacy codes: CERFACS has successfully developed solvers for PDEs. This is the case of the LES reacting flow solver AVBP. Preparing such codes for future architectures is a continuing task at CERFACS. A related field of development for these legacy codes is fully adaptive meshing techniques to hide all meshing tasks for end users.

B – Future methods and solvers: Research in numerical PDEs is progressing rapidly. CERFACS explores promising paths for future PDE solvers. A special example is the LBM which is already studied intensively at CERFACS in coordination with leading laboratories in the field (M2P2 in Marseille, FAU Erlangen). The LBM can be implemented efficiently on certain architectures and is especially suited for manycore accelerators. In this field, the ALGO and CFD teams work together. In addition to the LBM approach, work has been carried out on another equally promising approach: SDM (Spectral Difference Method which is a family of high-oder discontinuous approach). The latter makes it possible to obtain very accurate LES simulations (up to now spatial order up to ten have been tested) with a competitive cost compared to traditional approaches. CERFACS developed its own platform called JAGUAR and since 2018 CERFACS shares the ownership and the development of this solver with ONERA.


Thierry Poinsot officially entered the French Academy of Sciences

CERFACS |  8 November 2021

Thierry Poinsot officially entered the French Academy of Sciences on October 12. See presentation here :Read more

The AVBP code from CERFACS at the heart of for PRACE projects from the 23rd call

CERFACS |  30 September 2021

Cerfacs is involved in three PRACE projects of the 23rd call for which hour allocation runs from 01/10/2021 to 30/09/2022. Researchers from ECL/LMFA UMR5509 (Ecole Centrale de Lyon) and IMFT (UMR 5502) laboratories have earned projects entirely based on the use of the LES solver developed by Cerfacs AVBP and involve the support of experts from the CFD and COOP teams underling the importance and effectiveness of collaborations between French labs and Cerfacs. Alexis Giauque from ECL/LMFA UMR5509 (Ecole Centrale de Lyon) has obtained not only one but two PRACE projects! The first project LESFAN (RA0101, 30 000 000 CPU hours on Irene/Rome TGCC) is based on the use of AVBP in the turbomachinery version to study the generation of noise by a fan of a real airplane engine. The second, PRACE-EDGES (RA0101, 40 000 000 CPU hours on Irene/Rome TGCC) focuses on LES modeling of dens gas in complex geometries. To do so, the LMFA Team has developed advanced thermodynamic closures in AVBP allowing the direct simulation of such flows. Laurent Selle from IMFT (UMR 5502) has received CPU hours for the GASTON project (RA0061, 30 000 000 CPU hours on Marenostrum BSC) which aims to study the structure of hydrogen flames in porous materials. For this, IMFT and Cerfacs will perform coupled simulations considering the reactive flow with AVBP as well as the conduction in the porous medium with AVTP which is known to play an central role in the flame stabilization process. Carlos Perez Arroyo from IMFT (UMR 5502) received 16 Mh CPU hours on Joliot-Curie Skylake partition to support his project WONDER.Read more