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Adaptive Higher-Order Variational Methods for Aerodynamic Applications in Industry

Final Report Summary - ADIGMA (Adaptive Higher-Order Variational Methods for Aerodynamic Applications in Industry)

The main goal of the ADIGMA project was to further strengthen computational fluid dynamics (CFD) as a key enabler for meeting the goals of future air transportation by developing innovative numerical simulation techniques with significant improvements in efficiency, accuracy and reliability.

CFD has become a key technology in the development of new products in the aeronautical industry. Significant improvements in physical modelling and solution algorithms as well as the enormous increase of computer power have enable numerical simulations in all stages of aircraft development. However, despite the progress made in CFD, in terms of user time and computational resources, large scale aerodynamic simulations of viscous high Reynolds number flows are still very expensive and time consuming.

The ADIGMA project concentrated on technologies showing the highest potential for efficient higher-order discretisations. These are discontinuous Galerkin (DG) methods and continuous residual distribution (CRD) schemes. The main scientific objectives of the ADIGMA project were:
- Further development and improvement of key ingredients for higher-order space discretisation methods for compressible Euler, Navier-Stokes and RANS equations.
- Development of higher order space-time discretisations for unsteady flows including moving geometries.
- Development of novel solution strategies to improve efficiency and robustness of higher order methods, enabling large-scale aerodynamic applications.
- Development of reliable adaptation strategies including error estimation, goal-oriented isotropic and anisotropic mesh refinement and the combination of mesh refinement with local variation of the order of accuracy (hp-refinement).
- Utilisation of innovative concepts in higher-order approximations and adaptation strategies for industrial applications.
- Critical assessment of newly developed adaptive higher-order methods for industrial aerodynamic applications; measurement of benefits compared to state-of-the-art flow solvers currently used in industry.
- Identification of the best strategies for the integration as major building blocks for the next generation industrial flow solvers.

The competitiveness of higher-order methods to standard finite volume solvers was demonstrated for airfoil computations and 3D inviscid or laminar flows around rather simple configurations. Only limited research activities were devoted to the discretisation of the RANS equations with higher order methods, and it became clear that this effort is still in its infancy. A dedicated effort towards the industrialisation of the different higher-order methods is required and in particular the understanding of the discretisation procedure needs to mature. Moreover, although work was carried out to mitigate the resource usage of higher-order methods, further research needs to be invested in the area of algorithm optimisation and complexity reduction. Although within ADIGMA various methods and strategies were investigated and further enhanced to improve the solver efficiency of higher-order methods, the development of memory and CPU efficient solvers for large-scale industrial relevant applications still remains a major challenge.

The main achievements of the collaborative research project ADIGMA were:
- Significant progress in the development of adaptive higher-order methods for aerodynamic applications with high scientific output.
- Unique approach for critical assessment of innovative methods for industrial use.
- Creation of a comprehensive data base for performance assessment of advanced CFD methods.
- Successful demonstration of the potential and capabilities of higher-order methods.
- Identification of limitations and research directions for further industrialisation of higher order methods as well as.
- Significant improvement of the collaboration between academia, research organisations and industry on advanced CFD methods.

Despite the significant progress, it has to be mentioned that many achievements are still far from industrial use.