## Section: Application Domains

### Co-design for scalable numerical algorithms in scientific applications

Participants : Pierre Brenner, Jean-Marie Couteyen, Luc Giraud, Xavier Lacoste, Guillaume Latu, Salli Moustapha, Pierre Ramet, Fabien Rozar, Jean Roman, Pablo Salas, Xavier Vasseur.

The research activities concerning the ITER challenge are involved in the Inria Project Lab (IPL) C2S@Exa .

#### MHD instabilities Edge Localized Modes

The numerical simulations tools designed for ITER challenges aim at making a significant progress in
understanding of largely unknown at present physics of active control
methods of plasma edge MHD instabilities Edge Localized Modes (ELMs)
which represent particular danger with respect to heat and particle
loads for Plasma Facing Components (PFC) in ITER. Project is focused
in particular on the numerical modeling study of such ELM control
methods as Resonant Magnetic Perturbations (RMPs) and pellet ELM
pacing both foreseen in ITER. The goals of the project are to improve
understanding of the related physics and propose possible new
strategies to improve effectiveness of ELM control techniques. The
tool for the nonlinear MHD modeling (code `JOREK` ) will be largely
developed within the present project to include corresponding new
physical models in conjunction with new developments in mathematics
and computer science strategy in order to progress in urgently needed
solutions for ITER.

The fully implicit time evolution scheme in the
`JOREK` code leads to large sparse linear systems that have to be solved at
every time step. The MHD model leads to very badly conditioned
matrices. In principle the `PaStiX` library can solve these large
sparse problems using a direct method. However, for large 3D problems the CPU
time for the direct solver becomes too large. Iterative solution
methods require a preconditioner adapted to the problem. Many of the
commonly used preconditioners have been tested but no satisfactory
solution has been found.
The research activities presented in Section
3.3
will contribute to design
new solution techniques best suited for this context.

#### Turbulence of plasma particules inside a tokamak

In the context of the ITER challenge, the `GYSELA` project aims to
simulate the turbulence of plasma particules inside a tokamak. Thank
to a better comprehension of this phenomenon, it would be possible to
design a new kind of source of energy based of nuclear fusion.
Currently, `GYSELA` is parallalized in a MPI/OpenMP way and can exploit
the power of the current greatest supercomputers (e.g., Juqueen). To
simulate faithfully the plasma physic, `GYSELA` handles a huge amount
of data. In fact, the memory consumption is a bottleneck on large
simulations (449 K cores). In the meantime all the reports on the
future Exascale machines expect a decrease of the memory per core. In
this context, mastering the memory comsumption of the code becomes critical
to consolidate its scalability and to enable the implementation of
new features to fully benefit from the extreme scale architectures.

In addition to activities for designing advanced generic tools for
managing the memory optimisation, further algorithmic research will be
conduced to better predict and limit the memory peak in order to
reduce the memory footprint of `GYSELA` .

#### SN cartesian solver for nuclear core simulation

As part of its activity, EDF R&D is developing a new nuclear core
simulation code named `COCAGNE` that relies on a Simplified PN (SPN) method to compute
the neutron flux inside the core for eigenvalue calculations. In order
to assess the accuracy of SPN results, a 3D Cartesian model of PWR
nuclear cores has been designed and a reference neutron flux inside
this core has been computed with a Monte Carlo transport code
from Oak Ridge National Lab. This kind of 3D whole core probabilistic
evaluation of the flux is computationally very demanding. An efficient
deterministic approach is therefore required to reduce the computation
effort dedicated to reference simulations.

In this collaboration, we work on the parallelization (for shared and
distributed memories) of the `DOMINO` code, a parallel 3D Cartesian SN
solver specialized for PWR core reactivity computations which is fully
integrated in the `COCAGNE` system.

#### 3D aerodynamics for unsteady problems with moving bodies

ASTRIUM has developped for 20 years the `FLUSEPA` code which focuses on
unsteady phenomenon with changing topology like stage separation or
rocket launch. The code is based on a finite volume formulation with
temporal adaptive time integration and supports bodies in relative
motion.
The temporal adaptive integration classifies cells in several temporal
levels, zero being the level with the slowest cells and each level being
twice as fast as the previous one. This repartition can evolve during
the computation, leading to load-balancing issues in a parallel
computation context.
Bodies in relative motion are managed through a CHIMERA-like technique
which allows building a composite mesh by merging multiple meshes. The
meshes with the highest priorities recover the least ones, and at the
boundaries of the covered mesh, an intersection is computed. Unlike
classical CHIMERA technique, no interpolation is performed, allowing
a conservative flow integration.
The main objective of this research is to design a scalable version of
`FLUSEPA` in order to run efficiently on modern parallel architectures
very large 3D simulations.

#### Nonlinear eigensolvers for thermoacoutic instability calculation

Thermoacoustic instabilities are an important concern in the design of gas turbine combustion chambers. Most modern combustion chambers have annular shapes and this leads to the appearance of azimuthal acoustic modes. These modes are often powerful and can lead to structural vibrations being sometimes damaging. Therefore, they must be identified at the design stage in order to be able to eliminate them. However, due to the complexity of industrial combustion chambers with a large number of burners, numerical studies of real 3D configurations are a challenging task. The modelling and the discretization of such phenomena lead to the solution of a nonlinear eigenvalue problem of size a few millions.

Such a challenging calculations performed in close collaboration with the Computational Fluid Dynamic project at CERFACS.