Special Issue on High Performance Supercomputing (HPC) in Fusion Research 2020

The JOREK extended magneto-hydrodynamic (MHD) code is a widely used simulation tool for studying the non-linear dynamics of large-scale instabilities in divertor tokamak plasmas. The code is usually run with a fully implicit time integration allowing to use large time steps independent of a CFL criterion. This is particularly important due to the strong scale separation between transport processes and slowly growing resistive modes in contrast to fast time scales associated with MHD waves and fast parallel heat transport. For solving the resulting large sparse-matrix system iteratively in each time step, a preconditioner based on the assumption of weak coupling between the toroidal harmonics is applied. The solution for each harmonic matrix is determined independently in this preconditioner using a direct solver. In this article, a set of developments regarding the JOREK solver and preconditioner is described, which lead to overall significant benefits for large production simulations. The developments include the implementation of a complex solver interface for the preconditioner leading to the general reduction of memory consumption. The most significant development presented consists in a generalization of the physics based preconditioner to ‘mode groups’, which allows to account for the dominant interactions between toroidal Fourier modes in highly non-linear simulations. At the cost of a moderate increase of memory consumption, the technique can strongly enhance convergence in suitable cases allowing to use significantly larger time steps, and thus improving the overall time performance by more than a factor of 3.

When an incompressible fluid flows through a contraction in a conduit, the increase in the kinetic energy of the fluid is accompanied by a pressure drop. This pressure drop is not to be assimilated with head loss. If downstream the fluid encounters an expansion in the conduit, the energy conversion will take place in the opposite way. Therefore, when a geometrical singularity is analysed to assess its contribution to the pumping power requirements of the system, the whole mechanical energy transfer of the fluid in the singularity has to be taken into account, and not only the pressure variation. The first part of the present work establishes a method to obtain head loss coefficients in geometric singularities of hydrodynamic circuits using the results of computational fluid dynamics (CFD) calculations. These coefficients are of interest when modelling the whole system with a 1D system code, for instance. In the second part of the article, the method is applied to a more complex case, involving magnetohydrodynamic (MHD) phenomena. Thus, a prototypical channel singularity in a liquid metal circuit subject to a magnetic field is analysed. The layout is representative of a case that could be found in the liquid metal blankets to be used in nuclear fusion reactors. The influence of the MHD phenomena is studied and the differences with a purely hydrodynamic case are pointed out. The MHD analyses have been done in the Marconi High Performance Computing facility, using 48 cores, each case needing between one and two weeks to complete.

Three-dimensional nonlinear MHD simulations study the core collapse events observed in a stellarator experiment, Wendelstein 7-X. In the low magnetic shear configuration like the Wendelstein 7-X, the rotational transform profile is very sensitive to the toroidal current density. The 3D equilibrium with localized toroidal current density is studied. If the toroidal current density follows locally in the middle of the minor radius, the rotational transform is also changed locally. Sometimes, the magnetic topology changes due to appearing the magnetic island. A full three-dimensional nonlinear MHD code studies the nonlinear behaviors of the MHD instability. It was found that the following sequence. At first, the high-n ballooning-type mode structure appears in the plasma core, and then the mode linearly grows. The high-n ballooning modes nonlinearly couple and saturate. The mode structure changes to the low-n mode. The magnetic field structure becomes strongly stochastic into the plasma core due to the nonlinear coupling in that phase. Finally, the plasma pressure diffuses along the stochastic field lines, and then the core plasma pressure drops. This is a crucial result to interpret the core collapse event by strong nonlinear coupling.

In this work we present an implementation of accelerating the calculation of neutral gas flow in a single-null DEMO divertor configuration on a graphics processing unit (GPU), using the DIVGAS (divertor gas simulator) code. For comparison purposes, various types of GPUs will be used, which include pure GPUs for scientific calculations as well as GPUs for gaming purposes. The computation accuracy of the DIVGAS code on GPUs has been validated with the corresponding CPU-based benchmark case. To evaluate the performance gains, the computing time on each GPU against its sequential CPU counterpart has been compared. The measured speedups show that the GPU can accelerate the execution of the DIVGAS code by a factor of 60. The speedup of the DIVGAS code scales linearly with the corresponding double precision peak performance of the GPU as well as the GPU memory bandwidth. The parallelization approach presented here significantly reduces the cost of DIVGAS simulations and has the potential to scale to large CPU/GPU clusters, which could enable future applications, which focus on even more complex 3D neutral flow problems. The accelerated version of the DIVGAS code on GPUs is considered to be a major breakthrough in the reduction of the needed computational time for fusion related applications.

Understanding the behaviour of high-temperature plasmas is one of the main pillars in the development of fusion energy. It involves the development, validation, and use of several numerical models to describe complex physical processes and their interactions. Integrated modelling brings different models together, coupling them via suitable interfaces. Often, there is a need to include specific physics phenomena, such as magnetohydrodynamics, plasma turbulence or transport. They are computationally demanding and require modern supercomputers for their analysis. In such cases, the complexity of running integrated modelling workflows, including the use of supercomputers should be managed transparently, hidden to the final user. In this paper, we present and implement a scheme to tackle the execution of large fusion workflows on modern supercomputers using container technologies and a tool for their remote submission. We successfully packed in a container image a very complex environment: international thermonuclear experimental reactor (ITER) integrated modelling & analysis suite (IMAS). Moreover, we run high-performance computing codes up to 3072 cores with performance loss of 3%. The ITER H&CD worklfow was executed on Marconi and for the first time ran in a cluster without an installation of the IMAS framework. The presented capabilities have demonstrated the feasibility of our approach on Marconi-Fusion, the European High-Performance Computer for fusion applications and have tested a relevant application within the integrated modelling community.

In the fusion community, the use of high performance computing (HPC) has been mostly dominated by heavy-duty plasma simulations, such as those based on particle-in-cell and gyrokinetic codes. However, there has been a growing interest in applying machine learning for knowledge discovery on top of large amounts of experimental data collected from fusion devices. In particular, deep learning models are especially hungry for accelerated hardware, such as graphics processing units (GPUs), and it is becoming more common to find those models competing for the same resources that are used by simulation codes, which can be either CPU- or GPU-bound. In this paper, we give examples of deep learning models—such as convolutional neural networks, recurrent neural networks, and variational autoencoders—hat can be used for a variety of tasks, including image processing, disruption prediction, and anomaly detection on diagnostics data. In this context, we discuss how deep learning can go from using a single GPU on a single node to using multiple GPUs across multiple nodes in a large-scale HPC infrastructure.

Electromagnetic turbulence is addressed in tokamak and stellarator plasmas with the global gyrokinetic particle-in-cell codes ORB5 (E Lanti et al, Comp. Phys. Comm., 251, 107072 (2020)) and EUTERPE (V Kornilov et al, Phys. Plasmas, 11, 3196 (2004)). The large-aspect-ratio tokamak, down-scaled ITER, and Wendelstein 7-X geometries are considered. The main goal is to increase the plasma beta, the machine size, the ion-to-electron mass ratio, as well as to include realistic-geometry features in such simulations. The associated numerical requirements and the computational cost for the cases on computer systems with massive GPU deployments are investigated. These are necessary steps to enable electromagnetic turbulence simulations in future reactor plasmas.