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Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics

Periodic Reporting for period 2 - AROMA-CFD (Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics)

Reporting period: 2017-11-01 to 2019-04-30

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, the latter with a finite element full order solver, with applications also in multi-physics, thanks to multi-phenics packages ( Several other packages have been created and are available to provide basic tools in (shape) parametrisation, data assimilation, and non-intrusive model reduction 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.
The first 30 months for ERC AROMA-CFD have been smooth and important in setting properly several tasks. Recruiting at post-doctoral/post-master level was completed after 7 months (4 positions), several post-grad fellowship were awarded too to enhance the project set up (6 research prelauream fellowships and 2 postgrad/pre-doc fellowships, according school’s regulations).
All the research tasks have been activated and set up: 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 well interacting. Task 1 is more developed at the state of the art. Some of the subtasks are particularly growing in term of activities (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.
In Task 3 several advances were accomplished concerning the open software libraries development (ITHACA). Several releases of software packages have been done (see 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, ETHZ, Houston, Toronto, Florida State, Stuttgart, 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).
A project website has been created at 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).
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. 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 planned in Task 2, which is under development. Task 3 has already provided some outputs with open source software packages.
More efforts have been devoted to reduction in parameter space, as well as turbulent flows to increase the applicability of the methodology.
Graphical abstract AROMA-CFD
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