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arXiv · 1907.10549

A Reduced-Order Shifted Boundary Method for Parametrized incompressible Navier-Stokes equations

Efthymios N. Karatzas·Giovanni Stabile·Leo Nouveau·Guglielmo Scovazzi·Gianluigi Rozza
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Abstract

We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three-parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

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Efthymios N. Karatzas, Giovanni Stabile, Leo Nouveau, Guglielmo Scovazzi, Gianluigi Rozza. 2019-07-23. A Reduced-Order Shifted Boundary Method for Parametrized incompressible Navier-Stokes equations. https://doi.org/10.1016/j.cma.2020.113273

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