Removing splitting/modeling error in projection/penalty methods for Navier-Stokes simulations with continuous data assimilation

TL;DR

This paper demonstrates that continuous data assimilation can effectively eliminate splitting and modeling errors in projection and penalty methods for Navier-Stokes simulations, leading to more accurate long-term solutions.

Contribution

It introduces a method to use CDA to correct errors in projection and penalty schemes for Navier-Stokes equations, improving their accuracy.

Findings

CDA removes splitting and modeling errors effectively.

Proper parameter selection enhances long-term accuracy.

Numerical results confirm analytical predictions.

Abstract

We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modeling error (penalty) and splitting error (projection). We show analytically and numerically that with measurement data and properly chosen parameters, CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.