Non-linear Projection-Based Model Reduction for Turbulent Flow Problems
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Digital Twin applications have accelerated the requirement for rapid simulators. Conventional methods, despite their excellent accuracy and flexibility, are not suited for multiple-query applications, or time-critical cases. Model reduction techniques have shown to provide a great alternative. Still, depending on the parametrisation, or complexity of the underlying physical system, constructing a sufficiently rich reduced basis, or solving the respective online problem can be prohibitively costly. In this work we test non-linear reconstructions of otherwise underperforming reduced bases for the improvement of the ROM approximation. The process is structured in three distinct stages. The initial stage pertains to the sampling and the construction of a reduced basis via the Proper Orthogonal Decomposition (POD), performing Galerkin projection and solving the online problem. The second includes solving a modified version of the physical system for manipulations of the POD approximation and performing a decomposition, while the final step solves the combined problem for the augmented approximation. Finally, the performance of the proposed strategy is tested using numerical experiments of parametrised turbulent flow around aerofoils.