Reduced order models for generalized Newtonian fluid flows
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We present a parametrized projection-based model reduction technique for generalized Newtonian fluids and some applications. The proposed technique is based on the Proper Orthogonal Decomposition and the Variational MultiScale methods. The technique merges an incompressible Navier-Stokes model reduction method and stabilization techniques for generalized Newtonian and non-Newtonian fluids. We apply the method in a set of parametrized time-dependent problems which as usual involves an offline-online implementation. We use a finite element method for the space discretization and finite differences for the temporal discretization. We use the variational multiscale approach as a stabilization technique for both the high fidelity and the reduced order model. And for the construction of the basis, we follow a variation of a higher-order singular value decomposition
