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A domain decomposition non-intrusive reduced order model for turbulent flows. (English) Zbl 1411.76072
Summary: In this paper, a new domain decomposition non-intrusive reduced order model (DDNIROM) is developed for turbulent flows. The method works by partitioning the computational domain into a number of subdomains in such a way that the summation of weights associated with the finite element nodes within each subdomain is approximately equal, and the communication between subdomains is minimised. With suitably chosen weights, it is expected that there will be approximately equal accuracy associated with each subdomain. This accuracy is maximised by allowing the partitioning to occur through areas of the domain that have relatively little flow activity, which, in this case, is characterised by the pointwise maximum Reynolds stresses. A Gaussian process regression (GPR) machine learning method is used to construct a set of local approximation functions (hypersurfaces) for each subdomain. Each local hypersurface represents not only the fluid dynamics over the subdomain it belongs to, but also the interactions of the flow dynamics with the surrounding subdomains. Thus, in this way, the surrounding subdomains may be viewed as providing boundary conditions for the current subdomain. We consider a specific example of turbulent air flow within an urban neighbourhood at a test site in London and demonstrate the effectiveness of the proposed DDNIROM.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
Software:
ParMETIS; PETSc; Scikit
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