EUROfusion-theory and advanced simulation coordination (E-TASC): programme and the role of high performance computing

The fundamental research will be performed via a set of TSVV Tasks which are driven by the fusion R&D community and address questions or issues within the eight missions of the Fusion Roadmap. Each task will be closely linked to ACHs so that they can (a) benefit from the expertise in these Hubs, and (b) feed science and engineering breakthroughs into the ACHs to inform the development of software following well defined 'EUROfusion-standard' (c.f. sub-section 2.3).

One of the objectives of the TSVV tasks is to provide validated predictive capabilities by turning existing research codes into professional and widely used tools and by developing new codes to fill some gaps. The scientific vision is generally expected to be based on a multi-fidelity approach (ranging from first-principles-based models to reduced models that can be used in whole device modelling and for real-time control applications), including specific plans for verification, validation, and uncertainty quantification (VVUQ). In addition, it is understood that all participants of a given TSVV task share up-to-date development versions of the source codes and use a common development platform following modern software engineering standards. The software products developed in this context (EUROfusion standard software) are to be designed to benefit a wide range of users across EUROfusion, well beyond the team of code developers, with free availability (within EUROfusion) of up-to-date release versions of the source codes to be used for production runs.

The main research areas (addressing both tokamak and stellarator applications) that should be pursued are

• (a)  
  Core and pedestal plasma physics;
• (b)  
  Pedestal, scrape-off layer (SOL) and divertor plasma physics and plasma-wall interaction;
• (c)  
  Materials and neutronics modelling;
• (d)  
  Engineering and reactor design.

It is important to note that the research areas are all closely coupled. The core plasma couples to the SOL and divertor via the pedestal; this complex plasma system couples to the materials via the divertor and wall, both directly and via radiation (and neutrons in ITER and DEMO), while the materials choices, the need to breed tritium and the divertor design (for example) influence the engineering design. While E-TASC will seek to make new physics, technology and engineering advances in each of the areas at relatively high fidelity and rigor, it should also support a parallel activity to develop a framework that ultimately, but progressively, works towards integration of all aspects towards whole devices modelling.

A key element in the implementation of the E-TASC approach consists of setting up ACHs in several EUROfusion labs, involving fusion theorists, applied mathematicians, experts in high-performance computing, as well as experts in data science and intelligent systems. ACHs activities call for a more focused and centralized approach. The ACHs are expected to provide essential expertise and support in scientific computing and software engineering for the E-TASC initiative and for the entire EUROfusion Theory and Simulation Programme (plasma physics, fusion materials research, and fusion engineering) as highlighted in the EUROfusion roadmap. ACHs will also help develop a suitable portfolio of EUROfusion standard software for the European R&D programme in support of ITER, DEMO, HELIAS and associated facilities. This support should include advanced computational techniques for high-performance computing on emerging Exascale hardware. This programme will support a multi-fidelity approach that encompasses:

• (a)  
  large-scale first-principles modelling on high-end supercomputers (towards Exascale);
• (b)  
  intermediate-scale first-principles and integrated modelling on mid-range platforms;
• (c)  
  fast simulators, or reduced models, that can be used for whole device modelling on small computers and in systems codes;
• (d)  
  database management (e.g. simulation and multi-machine databases) and data visualisation.

Each ACH will be organized around a limited set of specific, fusion-relevant themes in computer science, scientific computing, data management, code integration, and software engineering. To cover the EUROfusion requirements, the support provided by the ACHs have been classified into three categories:

• Cat. 1—High Performance Computing: scalable algorithms, code parallelization and performance optimization, code refactoring, GPU-enabling, preparing codes for Exascale etc.
• Cat. 2—integrated modelling and control: code adaptation to the integrated modelling and analysis suite (IMAS) format to support both plasma operation and research activities on ITER, IMAS framework development, code integration etc.
• Cat. 3—data management: open access, data management, data analysis tools, aspects of artificial intelligence and VVUQ etc.

The IMAS system, based on a machine-generic data dictionary (Imbeaux et al 2015), is a key standardization tool for E-TASC and EUROfusion data and code integration. Indeed, it has proven to be an efficient platform for multi-facilities data analysis, verification and validation and for multi-codes integration. Various tools have been recently developed for the mapping of experimental data into IMAS interface data structure for the different EUROfusion tokamaks (Romanelli et al 2020) which will facilitate model validation and data analysis across different facilities. Finally, to enable the large scale numerical simulations essential for the programme, EUROfusion will continue to support a dedicated High Performance Computing platform. This includes support for the centralized integrated modelling computing platform—the so-called Gateway.

The expertise and skill sets differ for the TSVV Tasks and the ACHs. For the TSVV Tasks, the teams will come largely from the fusion community, and be a mix of theoretical, experimental and computational scientists and engineers; this is where the frontier, community-led fusion science and technology is performed. ACHs may require some fusion-specific expertise, but will largely be formed of software engineers and computer scientists; this expertise will apply frontier computer science to fusion problems and our EUROfusion-standard software.

Within E-TASC, two types of software are distinguished. On the one hand, the 'research software' is typically developed within the TSVV tasks or in the broader community. It tends to aim at addressing specific scientific or engineering questions and has a user base that often does not extend much beyond the code development team (although there are exceptions). The majority of the current EUROfusion software falls in this category, and while this will continue to play an important role in the future, it is clear that several significant challenges ahead—like supporting or even guiding ITER operation and DEMO design—call for a more systematic approach. Consequently, E-TASC will provide the platform and support to develop the so-called EUROfusion-standard software, taking the development, dissemination, and exploitation of fusion software to a new level.

EUROfusion-standard softwares will be developed by applying a very rigorous and consistent quality assurance process across all E-TASC activities; it will be designed to benefit a wide range of users across EUROfusion, well beyond the team of code developers, and will adhere to the following guidelines and criteria:

• free availability (within EUROfusion) of an up-to-date release version of the source code used for production runs;
• good software engineering practices (continuous integration, version control, regression/unit testing, shared development rules etc);
• high-quality code documentation via user manuals and reference publications (including, in particular, a detailed description of the underlying model);
• excellent support of users, co-developers, and support staff within EUROfusion (via contact person, mailing list, issue tracker etc);
• specific plans for code verification and validation including aspects of uncertainty quantification;
• user-friendly, intuitive interfaces and visualisation/post-processing tools, including interfaces to the IMAS Data Dictionary (where applicable);
• specific plans for code dissemination and user training within EUROfusion.

The development of EUROfusion standard softwares is to be primarily executed by the ACHs, using tight feedback loops involving the main code authors including physicists and engineers in the TSVV Tasks. In some cases, this software is to be developed from scratch, while in many instances the new codes will be developed and refactored from existing codes to become part of the EUROfusion-standard software suite.

This TSVV task addresses one of the grand challenges of fusion research: the ability to predict the transition from L-H confinement regime and its various characteristics. The long-term goal is to develop a validated predictive capability of the L-H transition including pedestal physics and the mitigation or avoidance of edge localized modes in the context of a multi-fidelity approach, from gyrokinetic (GK) to reduced models for ultimately real-time application.

In the first phase (2019–20) of the project, the focus was on using GK simulation and theory (e.g. Jenko et al 2005, Brizard and Hahm 2007, Falchetto et al 2008, Garbet 2010, Krommes 2012) to characterize the L-mode edge and H-mode pedestal just before and after the L-H transition and on investigating the sources and dynamics of the radial electric field leading to an improved confinement regime. The task is exploiting the state-of-the-art in GK simulation of the tokamak edge, developing reduced models, while addressing key aspects of Verification, Validation, and Uncertainty, Quantification. As summarized in figure 2, the overall project structure is sub-divided in five main pillars leading to an overall vision for integration beyond 2021:

• (a)  
  GK advancements for tokamak edge;
• (b)  
  L-mode characterization prior to L-H-transition;
• (c)  
  Study H-mode pedestal after L-H transition;
• (d)  
  Investigate the plasma radial electric field (E_r) sources & dynamics;
• (e)  
  Address key aspects of VVUQ.

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All the activities performed within this broad task cannot be reviewed here, but two typical examples of the work performed are provided below: (a) on the investigation of the radial electric field dynamics, and, (b) on the validation aspects on JET.

In the first example, it has been shown in GK simulations with the GYSELA code (Grandgirard et al 2016) that a radial electric field well develops in simulations performed with an axi-symmetric limiter by comparing cases with and without limiter (Dif-Pradalier et al 2020). GYSELA models the ions and trapped electrons gyro-kinetically in the core and edge regions as well as the closed/open field line transition and the SOL through the introduction of a simplified limiter mimicking the role of a heat and momentum sink. A spontaneous radially-localized shear layer develops at the transition from closed to open field lines only with the limiter and with an interface to the SOL. The shear in the radial electric field is associated with the mild steepening of the pressure profile. The spontaneous emergence of a stable and localized transport barrier at the transition between closed and open field lines, is interpreted as a possible prelude to the formation of a pedestal in the first principles simulations as in tokamaks experiments.

The second example is the more systematic exploitation of GK simulations to interpret the structure of the Joint European Torus (JET) ²⁷ plasma pressure pedestals with the ITER Like Wall (ILW, tungsten divertor and beryllium chamber, reference e.g. Pamela et al 2007, Matthews et al 2011) for different levels of applied power and injected neutral gas at the plasma boundary. Indeed, ITER-baseline plasmas at JET-ILW have been limited to lower pedestal electron temperatures compared to their JET-C (carbon-wall) counterparts (e.g. Frassinetti et al 2019). As a consequence, more heating power to achieve good pedestal performance is required with the ILW compared to C-wall. In addition, high fuelling is required with the JET-ILW to mitigate the W accumulation effect that further degrades the pedestal. Understanding the fundamental structure of the JET pedestal with a metallic wall is essential for extrapolating the results towards ITER with a similar selection of wall materials (Hatch et al 2019). In this context, the local GK calculations with the gyrokinetic plasma turbulence code GENE (Gyrokinetic Electromagnetic Numerical Experiment) (Jenko et al 2000) have been performed from a series of JET-ILW type I ELMy H-modes discharges operating with similar experimental inputs but at different levels of power and gas fuelling (Chapman et al 2021). It has been shown that the dominant slab-electron temperature gradient (ETG) driven modes (with high k_//) combined with neoclassical ion heat transport can account for the transport power loss across the pedestal when this can be measured in several of these JET discharges.

Understanding the processes governing runaway electrons (RE) generation during MMI is crucial for interpreting existing disruption mitigation experiments and for the design of an effective disruption mitigation system in ITER, where RE currents of several Mega-Amperes can severely damage the plasma-facing components. The long-term objective of this TSVV task is to develop

• (a)  
  a comprehensive theoretical-numerical model framework to reliably predict RE dynamics in disruptions with non-equilibrium atomic physics for medium size tokamaks, JET, JT60-SA and ITER;
• (b)  
  a model of RE mitigation by MMI and suggestions for improving RE mitigation scheme;
• (c)  
  a framework for the validation process against experimental data by developing synthetic radiation diagnostic tools.

Integrated simulation of RE requires computationally expensive kinetic models that are self-consistently coupled to the evolution of the background plasma parameters. The computational expense has been reduced by using parameterized RE generation rates rather than solving the full kinetic problem, Hesslow and co-workers (Hesslow et al 2019a; 2019b) have developed an improved and reduced model for the Dreicer generation rate for a wide range of plasma parameters and impurities. The need to include screening effects in partially ionized plasmas is important to simulate disruption mitigation scenarios with MMI to mitigate the disruption effects. For this purpose, a multilayer neural network has been trained on data obtained from kinetic simulations to accurately estimate the runaway generation rate. By implementing it in a fluid RE modelling tool(s), it has been shown that the improved generation rates lead to significant differences in the self-consistent runaway dynamics as compared to the results using the previously available formulas for the runaway generation rate. Numerical solutions of the coupled equations of runaway generation and electric-field diffusion (e.g. GO model by Smith et al 2006) in a JET-like disruptive scenario has shown that the plateau runaway current was significantly reduced when using the runaway generation rate by the neural network instead of the Connor–Hastie formula (Connor and Hastie 1975). The results demonstrate the need to account for partially ionized atoms for realistic modelling of Dreicer generation.

In this context, integrated transport simulations of the plasma disruption (induced by massive gas injection) up to the established RE beam have been performed and validated in an ASDEX Upgrade experiment (Linder et al 2020). A fluid approach has been used for calculating the evolution of the plasma background (with the ASTRA code (Fable et al 2013)), the impurities (with the STRAHL code (Dux et al 1999)) and the runaway electrons beam where the RE growth and decay physics processes have been captured in presence of partially ionized high-Z impurities (with REGIA for RE Generation In Astra (Linder et al 2020)). It was found that the generation of REs in the ASDEX Upgrade discharge #33108 is described reasonably well within the fluid simulation (Linder et al 2020) by reproducing the final RE current obtained experimentally when the impact of partially ionized impurities on RE generation are included through application of the models by Hesslow et al (2019a), Hesslow et al (2019b). Hence, the simulations reproduce reasonably well both the evolution of the RE current and Hard x-ray measurements. Finally, it was noted that the model will have to be updated for the simulation of the JET or ITER Deuterium-Tritium experiments to also include RE generation mechanisms due to nuclear processes (e.g. tritium decay, Compton scattering).

Synthetic radiation diagnostic tools are essential for an accurate validation of the RE simulation against experimental measurements. The synchrotron radiation emission of the relativistic RE is measured in order to diagnose characteristics of the RE distribution function. Synthetic synchrotron radiation diagnostics have been developed to be compared directly to experimental data. Analyses of visible-light camera images of the synchrotron emission from RE have been performed for the ASDEX Upgrade discharge #35628 (Hoppe et al 2021) as shown in figure 3. In the forward modelling (solution of a fluid-kinetic equation system) the electron kinetic code CODE (Landreman et al 2014, Stahl et al 2016) and the fluid code Go (Smith et al 2006, Fehér et al 2011, Papp et al 2013) have been coupled. This approach allows to self-consistently solve Faraday's law for the electric-field evolution together with the rate equations for the evolution of the temperature and ion charge states in the presence of cold argon impurities. This coupled kinetic-fluid framework permits the simulation of the evolution of the runaway electrons distribution function (radius, energy, pitch) during the current-quench and runaway plateau phases of the disruption, with a prescribed runaway seed profile which is assumed to have survived the thermal quench. The simulations reveal that the evolution of the runaway distribution is well-described by a two-component process: an initial hot tail seed population, which is accelerated to energies ranging between 25 and 50 MeV during the current quench, together with an avalanche runaway tail which has an exponentially decreasing energy spectrum. During the runaway plateau, the evolution of the runaway distribution is found to mainly consist of pitch-angle relaxation. It has been concluded that, although the avalanche component carries the vast majority of the current, it is the high-energy seed-remnant that dominates the synchrotron emission.

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This specific and well-focused TSVV task is addressing in a synergetic manner activities for both stellarators and tokamaks configurations (Velasco et al 2020). Indeed, numerical tools developed for three-dimensional, 3D, magnetic stellarator configurations can be adapted for solving specific aspects of tokamak physics. For instance, an accurate calculation of radial neoclassical transport is important for both tokamaks and stellarators. Intrinsically, 3D magnetic configurations of stellarators lead to specific neoclassical transport regimes that produce radial energy transport comparable, and often larger, than the turbulent fluxes. In tokamaks, deviation from axi-symmetry can result in a significant neoclassical damping of the toroidal rotation and change the confinement properties of the tokamak configuration. A fast code for the calculation of the toroidal neoclassical viscosity in present and future tokamaks such as ITER has therefore been developed by adapting numerical tools developed for stellarators to tokamaks with broken toroidal symmetry (e.g. toroidal magnetic ripple or resonant magnetic perturbations).

Recent results include the derivation of the equations that allow a fast and accurate computation of the radial neoclassical transport in low collisionality regimes, and the development of numerical tools to solve such equations. KNOSOS (Velasco et al 2021) is a freely-available (Velasco 2022) open-source code that provides a fast computation of low collisionality neoclassical transport in 3D magnetic confinement devices by rigorously solving the radially local bounce-averaged drift kinetic equation coupled to the quasi-neutrality equation. KNOSOS incorporates physics ingredients often neglected in local 3D neoclassical simulations, such as the components of the magnetic drift and the electric field that are tangent to magnetic surfaces, as well as the effect of the local magnetic shear. It has been shown that, by characterizing plasmas of several devices, KNOSOS reproduces (where applicable) the results of standard neoclassical codes while being typically two orders of magnitude faster. In addition, KNOSOS describes the superbanana-plateau transport regime of stellarators and non-axisymmetric tokamaks by retaining the effect of the component of the magnetic drift that is tangent to magnetic surfaces. Therefore, KNOSOS provides the calculation of the NTV in tokamaks with broken axi-symmetry configurations at low value of plasma collisionality. Several applications of KNOSOS are planned for stellarators and tokamaks, including detailed validation activities against experimental data for Wendelstein 7-X, LHD and ASDEX Upgrade. As a preliminary application, a comparison of the electron NTV calculated with NEO-2 (Kernbichler et al 2016) and KNOSOS for one ASDEX Upgrade discharge is illustrated in figure 4. The preliminary results indicate a good agreement between the two codes outside mid-radius with a computing time ∼10 s per flux-surface. It should be pointed out that activity is ongoing to understand the difference between the two codes for tokamak geometry, and, to ultimately improve the calculation inside the normalized plasma radius of 0.5.

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Neutral gas physics and neutral interactions with the plasma background are key aspects for describing the plasma edge and divertor physics in present and future tokamak or stellarator facilities. Indeed, predictions of ITER and future fusion reactor plasma edge and plasma-wall interaction behaviour rely on the modelling of the detachment phenomenon which are essential for solving the power exhaust challenges of the mission 2 of the fusion roadmap (c.f. also next sub-section 3.5).

The EIRENE 3D Monte-Carlo code (Reiter et al 2005) is used worldwide to model neutral transport in tokamaks (e.g. Medium Size Tokamaks, EAST, JET, JT60-U, JT-60SA, ITER) with and without magnetic perturbations, stellarators and helical devices (e.g. TJ-II, LHD, W7-X). EIRENE is coupled in different code packages such as SOLPS-ITER (Wiesen et al 2015) and SOLEDGE2D-EIRENE (Bufferand et al 2015). The objective of this recently initiated TSVV task is to improve the accuracy and performance of various approaches within EIRENE to simulate the neutral gas dynamics for practical applications to ITER and fusion reactor. It should be noted that modelling of transients which require time-dependent simulations poses additional challenges for the code performance. Moreover, including the louvre areas and pump ducts into the simulation volume was proven to be significant for the pumping speed and penetration of neutrals modelling including molecules into the plasma with isotopic effects. An accurate prediction of heat and particle fluxes outside the divertor plates also necessitate an extended grid allowing the far-SOL flows to be included into the modelling (Dekeyser et al 2021).

The Monte-Carlo approach performs well in cases where neutrals can be treated as kinetic particles with large mean-free paths between collisions. However, the neutral collisionality will increase dramatically in high-density regions leading to much more complex trajectories with simulations of competing atomic and molecular reaction chains processes. This requires an increase of the codes performance by several orders of magnitude. Part of the effort may consist of 'brute force' acceleration of codes by refactoring and parallelization schemes. However, this will probably not be sufficient for computationally challenging simulations in high-collisional edge regions as anticipated for ITER, DEMO and fusion reactors. Fortunately, for these application domains, it is possible to treat a fraction of neutrals in a fluid approximation which is computationally efficient. It is worth noting that this approximation, known as advanced fluid neutral (AFN) approach, has been significantly improved (Horsten et al 2017). It is important to derive a hierarchy of models suitable for regions with various collisionalities and other relevant parameters ranging from pure kinetic (most accurate) to the fluid approach for performance. An illustration of the overview of the hierarchy of models for the different simulation approaches of the neutral gas dynamics is shown in a schematic diagram (c.f. figure 5). The overview of these methods including their relation and advantages is given in (Borodin et al 2021). The diagram graphically illustrates the trade-off that needs to be found between the model accuracy (fully kinetic model) and the computational efficiency (fluid model). In this context, hybrid fluid-kinetic models could provide an optimum between accuracy and computational efficiency for simulating ITER and DEMO. The intermediate hybrid approaches combine the advantages of both. For instance the so-called micro-macro hybrid (mMH) approach based on using a fraction of simulations done kinetically as a sort of correction term is seamless in the volume and theoretically fully equivalent to the full kinetic approach by the accuracy. The so-called spatial approach based on segregation of AFN and kinetic domains in space is a trade-off between accuracy and performance.

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It has already been shown that hybrid fluid-kinetic approaches developed for the computational fluid dynamics-EIRENE packages combine acceptable computing performance with model accuracy approaching full kinetic simulations as shown in figure 6 with results obtained with the so-called mMH method in a slab geometry approximation.

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Currently, the efforts are focused on the

• (a)  
  Fundamental and basic development of the hybrid approaches;
• (b)  
  Comparison against full-kinetic simulations to determine the gain in computational speed-up and optimal parameters;
• (c)  
  Assessment of the hybrid approach and their suitability for modelling new physics and operating domains at high edge collisionality in ITER or DEMO;
• (d)  
  Unification of the methods allowing e.g. combined mMH and spatially hybrid (SpH) simulations;
• (e)  
  Error assessment including particular contributions (bias, cancelation and statistical noise).

The OpenMP-MPI code parallelization and optimisation of the modelling atomic and molecular processes should progress in parallel. However, it should be stressed that the optimization procedure may depend on the final selection of the hybrid fluid-kinetic scheme.

The aim is to develop a neutral gas code (EIRENE) that provides a hierarchy of neutral (and trace ion) models with guidelines and automatic tools for hybridisation and parallelisation parameter optimisation to allow the end user to decide on an appropriate level of accuracy and performance depending on the problem to solve.

It is widely acknowledged that in the extreme conditions (in terms of exhaust and neutron fluxes) of a reactor relevant machine, handling the plasma exhaust towards the material surfaces of the device is of crucial importance, i.e. the so-called Mission 2 (Heat-Exhaust systems) of the 2012 and 2018 fusion roadmap (Fusion Electricity—A roadmap to the realisation of fusion energy 2012 and European Research Roadmap to the Realisation of Fusion Energy 2018). To extrapolate present day results to ITER and DEMO with sufficient confidence, adequate predictive capabilities, based on first principles insight, should be obtained through the development of both theoretical models for the plasma edge and innovative numerical codes applicable to the new generation of High Performance Computer (HPC). An effort in this direction must take into account the challenges of the particular operation conditions for DEMO and future fusion reactors, which are not encountered in current experiments and therefore even less often properly modelled.

High performance computing is evolving at a fast pace towards Exascale capabilities, which will allow unprecedented performance for scientific codes and these advances must be intercepted by the fusion community building on the existing effort. This challenging TSVV task is aimed at producing an agile software framework for ultimately developing a European edge and boundary code that builds on past experience and existing codes, and adopts a multi-fidelity approach that is able to exploit computational advances and perform simulations in conditions more relevant to ITER and DEMO. The task has included requirements analysis, software architecture and high-level design of the main modules with an overall picture of their interaction, identification of optimal algorithms, and creation of modular applications to test the scalability of the proposed solutions. This is to ensure predictive capability for heat and particle exhaust up to reactor relevant conditions by following a multi-fidelity approach with a hierarchy of models allowing users to optimize fidelity versus the computing time depending on the application. For large and high fidelity cases the codes(s) should be designed to run on Exascale HPC architectures with an objective of typically one month duration simulations for the most advanced first-principle simulations. The long-term scope of the task is to simulate the coupled plasma and neutral particles physics (c.f. section 3.4) in the SOL and in the region inside the separatrix in realistic 3D geometry with self-consistent cross-field turbulent transport.

In the initial phase of the project performed in 2019 and 2020, only part of the full programme has been realized and the initial focus has been on the definition of the physics basis and on the specification of the high-level design leading to the development of a reduced number of core modules of the code to test its potential capabilities and scalability. In this initial period, particular attention has been devoted to transfer any original concept to the suite of existing European edge codes, with the aim of maintaining their unique features during the period of development of the European edge and boundary code. The key challenges and initial results for this ambitious task are summarized below:

• (a)  
  Developing plasma models compatible with reactor conditions: for instance, the simulations should deal with four decades of collisionality range from the divertor to the pedestal which is beyond the domain of applicability of standard fluid models. Indeed, the applicability of Braginskii-like fluid models is questionable to describe the whole boundary region. In the context of the task, the recent development of the gyro-moment approach to the GK model has provided an ideal framework for the development of a multi-fidelity scheme to simulate the turbulent plasma dynamics in the boundary region of tokamak devices where collisions play an important role and cannot be ignored (Frei et al 2020 &, 2021, Bufferand et al 2021). Also, a new model of the high collisional plasma sheath has been developed (Tskhakaya 2021).
• (b)  
  Integrating the reactor relevant physics: additional physics is required in turbulence models for describing consistently the environment (neutrals, impurities...) (Tamain et al 2021, Bufferand et al 2022).
• (c)  
  Optimizing the codes for HPC application: during the pilot phase in 2019–2020, the focus was on optimization of common bottleneck of existing codes, i.e. the elliptic solvers for plasma potentials.
• (d)  
  Optimising algorithms and computational needs: assess and implement the advanced parallel discretization methods based on the flux coordinate independent approach (Hariri and Ottaviani 2013, Stegmeir et al 2016) for the reduction of computational needs. During the pilot phase in 2019–2020, the Hybrid Discontinuous Galerkin approach has been investigated.

Finally, it should be stressed that the ongoing development in computers performance and efficiency will be critical for the success of this challenging task. Indeed, for simulating the full 3D turbulence including the neutral and impurity physics in the SOL in proper realistic magnetic geometry of DEMO, the number of degrees of freedom (DOF) is typically two orders of magnitude higher compared to some of the largest computational fluid dynamics simulation as for instance the Peloton Project (∼2 billion of DOF) (Blocken et al 2018). Indeed, Tamain (2021) has estimated that the DOF is around 200 billion for solving the heat and particle exhaust up to the reactor relevant conditions and size. Therefore, the challenge of the simulation of the edge and boundary for reactor relevant devices could only be addressed by following a holistic approach combining advances in HPC, optimization of the algorithms and computational methods suited for HPC and improvement in the integration of the most advanced physics.