(i) High-performance computing

Advances in HPC hardware systems and related computer software are critically important to the advancement of the state of the art in CFD simulation, particularly for high Reynolds number turbulent flow simulations. HPC technology will probably advance along two separate paths. Ongoing development of exascale systems will continue through 2030 and represents the technology that will most probably provide the large increase in throughput for CFD simulation during this timeframe (http://www.exascale.org) [7]. However, novel technologies, such as quantum computing or molecular computing, offer a true paradigm shift in computing potential and must be carefully considered at strategic points in the overall development plan, even though the technology is at a very low maturity level today.

In considering the likely performance of HPC systems in the future, it is important to recognize that the same rate of performance improvement that has been maintained over the past several decades is unlikely to continue. Already, clock rates of the individual processing elements have remained nearly constant since 2007. The rate at which individual features shrink on an integrated circuit has also slowed significantly. In this sense, Moore's law, which is really an observation (and has been an engineering goal) about the rate at which feature sizes shrink, is already breaking down. Other issues, such as power consumption and heat dissipation, are limiting the performance of processors. To compensate for these issues, computer architects have been rapidly increasing the amount of parallelism and developing optimized but less general-purpose architectures. The largest current systems already have over one million cores and many use a combination of general-purpose CPUs and graphics processing units, which are optimized for stream computing. These issues lead to several observations: (i) a sustained exaFLOP (10¹⁸ operations per second on a CFD application) may not be achieved until 2020 or later, (ii) HPC systems in 2020–2030 will be characterized by heterogeneous hardware nodes, containing several types of specialized processing elements and deep memory hierarchies, and (iii) extreme degrees of parallelism, of at least a billion-way for an exaFLOP system, will be common. Current predictions are that a 30 exaFLOP system should be possible in 2030. Innovation in hardware is likely to change the details of the system (e.g. specialized processing elements and multilevel memory hierarchies) but not the general nature of the system. These systems, while able to run current algorithms and code, will not do so efficiently.

In order to properly address the HPC challenge, three specific thrusts must be considered. First, current simulation software must be ported in evolving and emerging HPC architectures with a view towards efficiency and software maintainability. Second, investments must be made in the development of new algorithms, discretizations and solvers that are well suited for the massive levels of parallelism and deep memory architectures anticipated in future HPC hardware [8,9]. Finally, increased access to the latest large-scale computer hardware must be provided and maintained, not only for production runs, but also for algorithmic research and software development projects, which will be critical for the design and validation of new simulation tools and techniques [10,11].

(ii) Physical modelling

Advances in the physical modelling of turbulence for separated flows, transition and combustion are critically needed to achieve the desired state of CFD in 2030 [8,12–17]. For the advancement of turbulent flow simulation, three separate tracks for research are proposed: RANS-based turbulence treatments; hybrid RANS/LES approaches where the entire boundary layer is resolved with RANS-based models, and the outer flow is resolved with LES models; and LES, including both wall-modelled (WMLES) and wall-resolved (WRLES).

RANS-based turbulence models continue to be the standard approach used to predict a wide range of flows for very complex configurations across virtually all aerospace product categories [13,18–21]. They are easy to use, computationally efficient and generally able to capture wall-bounded flows, flows with shear, flows with streamline curvature and rotation and flows with mild separation. For these reasons, as well as the fact that RANS models will remain as an important component in hybrid RANS/LES methods, their use will continue through 2030. An advanced formulation of the RANS-based approach, where the eddy viscosity formulation is replaced with the direct modelling of the Reynolds stresses, known as the Reynolds stress transport (RST) method [22], will in principle be able to capture the onset and extent of flow separation for a wider range of flows [23]. Continued investment in RST models is envisioned into the 2020 timeframe, including careful implementation, verification and validation of the most promising variants of these models into research and production CFD codes.

Hybrid RANS/LES methods show perhaps the most promise in being able to capture more of the relevant flow physics for complex geometries at an increasingly reasonable computational cost [24,25]. However, although hybrid methods are making their way into current design practice, several issues still exist. First, the prediction of any separation that is initiated in the boundary layer will still require improvements in RANS-based methods. Second, a seamless, automatic RANS-to-LES transition in the boundary layer is needed to enhance the robustness of these methods. Continued investment in hybrid RANS/LES methods to specifically address these two critical shortcomings will be required. Additionally, more effective discretizations and solvers designed specifically for LES-type problems must be sought. When combined with advances in HPC hardware, these three developments will enable continued reduction in the RANS region as larger resolved LES regions become more feasible.

Application of LES to increasingly complex flows is a very active research area [26]. Cost estimates of WRLES show scaling with Reynolds number of about Re^2.5_L while WMLES is about Re^1.3_L, with the costs being the same at Re_L of approximately 10⁵. For the typically higher Reynolds numbers and aspect ratios of interest to external aerodynamics, WRLES will be outside of a 24 h turnaround period even on 2030 HPC environments unless substantial advances are made in numerical algorithms. However, WRLES is potentially feasible in 2030 for lower Reynolds numbers and is a reasonable pursuit for many relevant aerospace applications, including many components of typical aerospace turbomachinery [27]. WMLES requires additional development of the wall-modelling capability [28]. As such, investments in LES research are needed with emphasis on (i) improved utilization of HPC including developments of numerical algorithms that can more effectively use future HPC environments and (ii) improved wall-modelling capability necessary for reliable WMLES.

Transition modelling is also a key area of investment, as an effective transition model would benefit RANS, hybrid RANS/LES and LES (by relieving mesh requirements in the laminar and transition regions). Thus, reliable and practical transition models must be developed and incorporated in the turbulence models being matured. The transition prediction method should be fully automatic, and be able to account for transition occurring from various mechanisms such as Tollmien–Schlichting waves, cross-flow instabilities, Görtler vortices and nonlinear interactions associated with bypass transition.

In the area of turbulent reactive flows, the development of a validated, predictive, multiscale combustion modelling capability to understand and optimize the performance of current and future fuels (including drop-in aviation alternative fuels) for advanced engines is needed. The principal challenges are posed by the small length and time scales of the chemical reactions (compared to turbulent scales), the many chemical species involved in hydrocarbon combustion, and the coupled process of reaction and molecular diffusion in a turbulent flow field. Current combustion modelling strategies rely on developing models for distinct combustion regimes, such as non-premixed, premixed at thin reaction zone and so forth. The predictive technology should be able to switch automatically from one regime to another, as these regimes coexist within practical devices. Furthermore, research should continue into methods to accelerate the calculation of chemical kinetics so that the CFD solution progression is not limited by these stiff ordinary differential equations.

Finally, investigation of radically novel approaches to physical modelling that may offer revolutionary changes in capabilities should be pursued. As an example, renormalization group theory [29,30] has been proposed as a general framework for turbulence and other multiscale physical modelling, although revolutionary advances have not materialized specifically for turbulence modelling. Nevertheless, advances in multiscale modelling such as systematic upscaling (SU) [31,32] offer the possibility for step changes in physical modelling capability and should be pursued in a measured manner.

(iii) Numerical algorithms

The development of novel numerical algorithms will be critical to achieving the stated CFD 2030 goals. Indeed, the proposed GC problems are sufficiently ambitious that advances in HPC hardware alone during the next 20 years will not be sufficient to achieve these goals. The focus of investment must be on discretizations and solvers that scale to massive levels of parallelism, that are well suited for the high-latency, deep memory hierarchies anticipated in future HPC hardware and that are robust and fault tolerant [9].

Discretization techniques such as higher order accurate methods offer the potential for better accuracy and scalability, although robustness and cost considerations remain [33]. Investment must focus on removing these barriers in order to unlock the superior asymptotic properties of these methods, while at the same time pursuing evolutionary improvements in other areas such as low dissipation schemes [34–36], flux functions and limiter formulations. Simultaneously, novel non-traditional approaches, such as lattice Boltzmann methods [37,38], should be investigated for special situations, particularly in low Mach number applications for complex configurations including computational aeroacoustics. Improved linear and nonlinear solvers must be developed, and here as well, the focus must be on highly scalable methods that are designed to be near optimal for the large-scale, time-implicit unsteady CFD and multidisciplinary design and optimization (MDAO) simulations anticipated in the future. These may include the extension of well-known matrix-based techniques, Krylov methods [39], highly parallel multigrid methods [40] or the development of completely novel approaches such as SU methods [31,32]. For complex multiscale physical systems, where equations are solved based on first principles at the microscopic level, SU methods provide a rigorous computational framework and rules to process the system at increasingly larger, macroscopic scales. Investment in discretizations and solvers must also consider the potential of these methods to operate on dynamically adapting meshes, to enable optimization procedures and to incorporate advanced uncertainty quantification capabilities. Longer term, high-risk research should focus on the development of truly enabling technologies such as monotone or entropy stable schemes [41,42] in combination with innovative solvers on large-scale HPC hardware.

With regard to uncertainty quantification, large-scale probabilistic CFD for aerospace applications should be emphasized. Initially, activity in this area should focus on enabling current aerospace CFD tools with well-known uncertainty quantification techniques, such as sensitivity analysis and propagation methods using adjoints and forward linearizations, non-intrusive polynomial chaos methods and other reduced-order model formulations [43,44]. Additionally, a concerted effort should be made to characterize important aerospace uncertainties and to make these available to the general research community. Improved error estimation techniques must be investigated and developed, given the known deficiencies of current approaches (including adjoint methods). Finally, longer term research must focus on statistical approaches such as Bayesian techniques for quantifying more accurately modelling and other nonlinear error sources [45].

(iv) Geometry and grid generation

Substantial new investment in geometry and grid generation technology will be required in order to meet the Vision CFD 2030 goals. In general, this area remains one of the most important bottlenecks for large-scale complex simulations. Focused research programmes in streamlined CAD access and interfacing, large-scale mesh generation and automated optimal adaptive meshing techniques are required. Efforts must concentrate on making mesh generation and adaptation less burdensome and, ultimately, invisible to the CFD process, while developing technologies that enable the Vision 2030 CFD capabilities, namely very large-scale parallel mesh generation, curved mesh elements for higher order methods [46,47], highly scalable dynamic structured and unstructured overset mesh technology [48,49] and in situ anisotropic adaptive methods for time-dependent problems. Advances in these areas will require incremental software development, combined with advances in fundamental areas such as computational geometry. Additionally, because significant technology currently resides with commercial software vendors, particularly for CAD interfaces and access, involving these stakeholders in the appropriate focused research programmes will be critical for long-term success.

(v) Knowledge extraction

Petascale and exascale simulations will generate vast amounts of data. In order to make effective use of large-scale simulations in aerospace engineering, focused research in data knowledge extraction is required. Ideally, this should contain three components: visualization, database management and variable fidelity, data integration techniques.

Methods to process and visualize very large-scale unsteady CFD simulations in real time, including results from higher order discretizations, are required to support the advanced CFD capabilities envisioned in 2030. Although many of the current efforts in maturing visualization technology are being led by commercial vendors, more fundamental research to directly embed visualization capabilities into production CFD tools optimized for emerging HPC platforms is needed to achieve real-time processing [50]. Moreover, the CFD capability in 2030 must provide the analyst with a more intuitive and natural interface into the flow solution to better understand complex flow physics and data trends and enable revolutionary capabilities such as computational steering, which could be used, as an example, for real-time virtual experiments or virtual flight simulation [51,52].

Foreseeing the capability of generating large databases with increasing computational power, techniques for rapidly integrating these databases, querying them in real time, and enhancing them on demand will be required, along with the ability to provide reliable error estimates or confidence levels throughout all regions of the database.

Finally, integrating high-fidelity simulation data with lower fidelity model data, as well as experimental data from wind tunnel tests, engine test rigs or flight-test data will provide a powerful approach for reducing overall risk in aerospace system design [53]. Techniques for building large-scale flexible databases are in their infancy, and range from simple software infrastructures that manage large numbers of simulation jobs to more sophisticated reduced-order models [54], surrogate models and Kriging methods [55,56]. The objective of research in this area should be to apply existing techniques to current CFD simulation capabilities at a large scale, while simultaneously performing foundational research in the development of better reduced-order models and variable fidelity models that are applicable to aerospace problems and can support embedded uncertainty quantification strategies.