Second order reduced model via incremental projection for Navier Stokes

TL;DR

This paper develops a second-order reduced-order model for incompressible flow simulations using incremental projection and POD, achieving efficient and accurate computations with proven stability and convergence.

Contribution

It introduces a novel second-order reduced model for Navier-Stokes equations using incremental projection and POD, with detailed stability and error analysis.

Findings

Second-order convergence in time demonstrated

Model achieves computational efficiency and accuracy

Numerical validation confirms theoretical results

Abstract

The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale computations. This work focuses on reduced-order modeling using incremental projection schemes for the Stokes equations. We present both semi-discrete and fully discrete formulations, employing BDF2 in time and finite elements in space. A proper orthogonal decomposition (POD) approach is adopted to construct a reduced-order model for the Stokes problem. The method enables explicit computation of reduced velocity and pressure while preserving accuracy. We provide a detailed stability analysis and derive error estimates, showing second-order convergence in time. Numerical experiments are conducted to validate the theoretical results and demonstrate computational efficiency.