# A Modular Regularized Variational Multiscale Proper Orthogonal Decomposition for Incompressible Flows

## TL;DR

This paper introduces a modular, post-processing VMS-POD method for incompressible flows, enabling easier implementation and independent stabilization tuning, supported by theoretical analysis and numerical validation.

## Contribution

It presents a novel decoupled, post-processing VMS stabilization integrated with POD for Navier-Stokes equations, enhancing flexibility and effectiveness.

## Key findings

- The method effectively stabilizes simulations of incompressible flows.
- Numerical tests confirm the theoretical properties and improved accuracy.
- The approach is easily incorporated into existing computational frameworks.

## Abstract

In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The projection-based VMS stabilization is added as a separate post-processing step to the standard POD approximation, and since the stabilization step is completely decoupled, the method can easily be incorporated into existing codes, and stabilization parameters can be tuned independent from the time evolution step. We present a theoretical analysis of the method, and give results for several numerical tests on benchmark problems which both illustrate the theory and show the proposed method's effectiveness.