A Modular Regularized Variational Multiscale Proper Orthogonal Decomposition for Incompressible Flows
For computational fluid dynamics practitioners, this provides an easy-to-implement stabilization technique for POD-based reduced-order models.
The paper proposes a modular post-processing VMS-POD method for incompressible flows that decouples stabilization from time evolution, enabling easy integration into existing codes. Numerical tests on benchmark problems demonstrate the method's effectiveness.
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.