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

## TL;DR

This paper introduces a reduced-order model for steady incompressible Navier-Stokes equations that leverages the Shifted Boundary Method and proper orthogonal decomposition, enabling efficient simulations with complex geometries without remeshing.

## Contribution

It presents a novel embedded reduced basis approach using the Shifted Boundary Method for parametrized geometries, avoiding remeshing and reference domain formulations.

## Key findings

- Validated convergence and efficiency on 2D examples
- Effective handling of geometrical parametrization
- Reduced computational cost for multiple parameters

## 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.