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Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics

Periodic Reporting for period 3 - AROMA-CFD (Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics)

Reporting period: 2019-05-01 to 2020-10-31

The framework under development within AROMA-CFD is going to provide attractive capabilities for several industrial and medical applications (e.g. aeronautical, mechanical, naval, off-shore, wind, sport, biomedical engineering and cardiovascular surgery as well), combining high performance computing (in dedicated supercomputing centres) and advanced reduced order modelling (in common devices), to guarantee real time computing and visualisation. A new open source software library for AROMA-CFD is under construction: ITHACA, In real Time Highly Advanced Computational Applications, enhancing current RBniCS educational and training capabilities. The first one at the moment is available with a finite volume full order solver and a spectral element method full order solver (and also a Discontinuous Galerkin solver is in progress), the latter with a finite element full order solver, with applications also in multi-physics, thanks to multi-phenics packages (mathlab.sissa.it/cse-software). Several other packages have been created and are available to provide basic tools in (shape) parametrisation (PyGem), data assimilation, and non-intrusive model reduction (EZyRB, PyDMD), uncertainty quantification (ATHENA) as well.

The aim of AROMA-CFD is to creation a team of scientists at SISSA for the development of Advanced Reduced Order Modelling techniques with a focus in Computational Fluid Dynamics (CFD), in order to face and overcome many current limitations of the state of the art and improve the capabilities of reduced order methodologies for more demanding applications in industrial, medical and applied sciences contexts. AROMA-CFD deals with strong methodological developments in numerical analysis, with special emphasis on mathematical modelling and an extensive exploitation of computational science and engineering. Several tasks of the project are under development to tackle fascinating problems and open questions in reduced order modelling: special emphasis on the study of bifurcations and instabilities in flows, important advances concerning the capability to deal with flows characterised by increasing Reynolds number, while guaranteeing the flow stability, moving towards (moderate) turbulent flows, considering more and more complex geometrical parameterisations of shapes as computational domains into extended networks, and reducing the parameter space too. A reduced computational and geometrical framework is under development for more and more complex nonlinear inverse problems, focusing on optimal flow control, shape optimisation and uncertainty quantification. Further, these advanced developments in reduced order modelling for CFD are going to be applied in multi-physics, such as fluid-structure interaction problems, and more general coupled phenomena involving inviscid, viscous and thermal flows, solids and porous media.
In the project development a more important role has been given to data, and the capability to incorporate them in wider and stronger mathematical setting like the one provided by optimal control, such that the assimilated data contribute to improve the mathematical models and results given by numerical simulation.

In this current setting also automatic learning is providing a more and more active role to methodological developments and to the improvement of numerical techniques.
After 54 months ERC AROMA-CFD is running smooth in properly carrying out several tasks. Recruiting at post-doctoral/post-master level was continuous, several post-grad fellowship were awarded too to enhance the project set up (with research prelauream fellowships and postgrad/pre-doc fellowships, according school’s regulations).
All the research tasks have seen important advances: both the ones related with methodological/numerical developments, as well as the ones more related with applications in industry and medicine. Tasks 1 and 2 are very well interacting. Task 1 was more developed at the state of the art. Some of the subtasks are particularly growing in term of activities and importance (like tasks 1.A 1.C 1.E or 2.A) some of them playing an important role in methodological developments for future applications (like task 1.B) or are requiring more investigation on some topics to be more and more efficient from the computational point of view (like task 1.D and 1.F). Many new ideas are going to be tested for task 1.A which demonstrated to lead the project with effort of increasing Reynolds number in parametric flows we considered by incorporating more and more advanced stabilisation techniques and then turbulence. Task 1.B become a challenge too in providing model reduction in very complex problems characterised by bifurcation phenomena.
In Task 3 several advances were accomplished concerning the open software libraries development (ITHACA). Several releases of software packages have been done (see mathlab.sissa.it/cse-software) both for RBniCS (training/educational initiative) and ITHACA (ITHACA_FV, for more expert users dealing with industrial applications, based on Finite Volume, and ITHACA-SEM based on spectral element methods).
Task 4 has been more related to workshop/conferences talks upon invitation and scientific cooperation (MIT, Paris VI, Virginia Tech, Houston, Toronto, Florida State, as well as Italian Institutions like PoliMi, PoliTo, Pavia etc). Also some outreach activities have been set thanks to some events like Trieste NEXT (European scientific research fair), ESOF 2020 or an important piece of news on RAI TGR Leonardo, a daily TV news dedicated to Science in Italy.
A project website has been created at people.sissa.it/grozza/aroma-cfd with the state of the art, people, publications, news, workshops, etc. A Twitter account has been created for the project AROMA_CFD, as well as for the software libraries, ITHACA_ROM and RBniCS, according the different target (expert scientists and newcomers/people in training, respectively).

AROMA-CFD projects is operating in a more data-enriched environment, with a wider focus on emerging needs in model order reduction for CFD.
Thanks to Task 2 more contacts with industrial and clinical partners highlighted on one side the need to go more deeper inside model order reduction for turbulent flow, on the other side a deeper focus on data and geometries, also in cardiovascular flows simulations. This was made possible also thanks to data driven techniques.
Concerning methodological developments, at the moment we have been more focused on Task 1, more activities have been carried out in Task 1.A as well as in Tasks 1.B and 1.C in dealing with loss of uniqueness of the solution, branching, instabilities as well as reduction in parameter space and geometrical parametrisation. These tasks are more related with the extension of classical methodologies to be better enriched and widened in a very complex setting. Activities in Tasks 1.D 1.E 1.F are more related with advanced and novel methodologies in view of more important applications, as the ones under development in Task 2. Task 3 has already provided some important outputs with open source software packages.
More efforts than originally planned have been devoted to reduction in parameter space, turbulent flows, as well as automatic learning techniques to improve the methodology.
Also optimal flow control framework has been more and more developed to provide a strong tool for simulation, data assimilation and inverse problem solutions.
Graphical abstract AROMA-CFD
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