Advanced Numerical Methods and HPC

Participants: V. Daru, O. Le Maître, F. Lusseyran, L. Mathelin, L. Pastur, B. Podvin, C. Tenaud

The increasing capabilities of computational infrastructures constantly provide new opportunities for both numerical and experimental flow studies, by allowing for high fidelity simulations and the storage and analysis of massive numerical or experimental data sets. In order to fully benefit from the opportunities offered by modern computational infrastructures, it is necessary to conduct researches on new numerical methods and algorithms. The topic "Advanced Numerical Methods and HPC" concerns a broad spectrum of challenges, including the development of numerical methods and schemes for more accurate and physically realistic simulations of complex dynamics, the implementation of existing solvers and algorithms on modern parallel computers, and the design of new algorithms anticipating the next generation of computational platforms. The outputs of these researches benefit to the topics of the AERO group (Unsteady Flows, Flow Control and Uncertainty Quantification) as well as to other projects of the ME Department and external partners / collaborators.

Advanced Numerical Methods. In the last years, the participants of the group have developed new simulation tools and solvers for high fidelity fluid flow predictions. An original low-Mach number formulation of liquid-gas flows (bubbles or droplets) has been proposed. It treats the gas phases as weakly compressible and the liquid phase as incompressible, through an appropriate extension of the thermodynamic pressure over the liquid domain. Several multi-resolution schemes and time-integrators have also been derived for reactive flow simulations, with the objective of capturing all relevant scales of the problem to maximize the numerical accuracy, while minimizing the computational cost by adapting dynamically the discretization effort. Finally, a new conservative coupling algorithm for deformable moving bodies (with possible fracturing) in a compressible viscous flow have been developed. This solver, dedicated to the simulation of impacting shockwaves on structures, relies on a (mass and energy) conservative coupling strategy combined with an Embedded Boundary Method.

High Performance Computing. The emergence of hybrid GPU / CPU architectures calls for an adaptation of the algorithms and computer codes to take full advantage of these new computational resources. The solvers of the code SunFluidh, developed at LIMSI for the resolution of the weakly compressible Navier-Stokes equations on structured grid, have been implemented and tested on hybrid multi-cores machines. The classical MPI approach (domain-decomposition) has been accelerated relying on multi-threaded GPU-based resolution of the local problems. Regarding the analysis of numerical or experimental flow fields, the extraction and tracking of Lagrangian structures from the Finite Time Lyapunov Exponents technique is a computationally very demanding task, particularly when treating large data sets. The related algorithms have been implemented on hybrid computers with GPU / CPU configurations, achieving computational time reduction by few orders of magnitudes.  Finally, the future exascale computing is anticipated through a prospective research activity on the design of algorithms resilient to soft and hard fault errors. Such errors are indeed expected to be more and more sensitive as the number of processors involved in the calculation becomes extremely large.

Wave patterns produced by the interaction of a strong shock wave with flapping doors: Density contours at time 0.375s. L. Monasse, 2011 © collaborative work between CEA-DAM, CERMICS-ENPC, and LIMSI-CNRS.

Main collaborations:

CERMIC-ENPC, CEA, EM2C-Centrale, Supélec, LRI-Paris Sud, Sandia, Duke University. 

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10 Research Teams
100 Researchers
40 Technicians and Engineers
60 Doctoral Students
70 Trainees

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