Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations

TL;DR

This paper explores using sparse polynomial interpolation as a novel model order reduction technique for the incompressible Navier-Stokes equations, demonstrating its effectiveness and advantages over traditional methods in handling high-dimensional problems.

Contribution

It introduces sparse polynomial interpolation as a new approach for model reduction in fluid dynamics, especially for complex geometries, and compares its performance with established reduced basis methods.

Findings

Sparse polynomial interpolation provides accurate reduced order models.

The method offers efficient offline-online splitting and reduced computational run time.

It effectively addresses the curse of dimensionality in parametric PDEs.

Abstract

This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial approximations and comparing with established reduced basis techniques. Two numerical models serve to access the accuracy of the reduced order models (ROMs), in particular parametric nonlinearities arising from curved geometries are investigated in detail. Besides the accuracy of the ROMs, other important features of the method are covered, such as offline-online splitting, run time and ease of implementation. The findings establish sparse polynomial interpolation as another instrument in the toolbox of methods for breaking the curse of dimensionality.