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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.

NEWS

CMIP6 debriefing workshop – May 2021: a stocktaking and foresight exercise that highlighted the major and long-term investment of the CNRM-CERFACS group in the latest climate model intercomparison international exercise

CERFACS |  9 June 2021

The participation of the CNRM-CERFACS group in the international coupled global climate model intercomparison exercise CMIP6 was debriefed on 10 and 11 May. Since the mid-1990s, the various phases of the Coupled Model Intercomparison Project (CMIP), supported by the World Climate Research Programme (WCRP), have enabled climate science to make significant progress, feeding into the IPCC reports, supporting regional climate modelling activities and downstream climate services. On the balance sheet, the participation of CNRM-CERFACS in the extremely demanding CMIP6 exercise has resulted in a large-scale, high-quality contribution in terms of climate simulations, thanks in particular to the strong commitment of researchers and engineers, the quality of support services and national and international collaborations. The activities mainly took place over the period 2013-2020. Initially, the production environment ("workflow") was set up and the coupled climate models were assembled by capitalising on the development of components (atmosphere, ocean and continental surfaces) carried out over the long term. The actual production of simulations was spread over 2018-2020. During the debriefing, perspectives (scientific objectives, model development, organisation) were drawn up with a view to a new participation of CNRM and CERFACS in CMIPRead more


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

CERFACS |  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

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