Variational Multiscale Evolve and Filter Strategies for Convection-Dominated Flows

TL;DR

This paper introduces a variational multiscale (VMS) approach to improve the evolve-filter (EF) stabilization method for convection-dominated flows, reducing overdiffusivity and enhancing accuracy in both full and reduced-order models.

Contribution

It proposes a novel VMS-based strategy with two algorithms to mitigate EF overdiffusivity, improving accuracy for high Reynolds number flows.

Findings

VMS-EFFC and VMS-EPFC algorithms outperform standard EF in accuracy.

The new methods effectively handle large filter radii without overdiffusivity.

Significant improvements observed in flow past a cylinder at Re=1000.

Abstract

The evolve-filter (EF) model is a filter-based numerical stabilization for under-resolved convection-dominated flows. EF is a simple, modular, and effective strategy for both full-order models (FOMs) and reduced-order models (ROMs). It is well-known, however, that when the filter radius is too large, EF can be overdiffusive and yield inaccurate results. To alleviate this, EF is usually supplemented with a relaxation step. The relaxation parameter, however, is very sensitive with respect to the model parameters. In this paper, we propose a novel strategy to alleviate the EF overdiffusivity for a large filter radius. Specifically, we leverage the variational multiscale (VMS) framework to separate the large resolved scales from the small resolved scales in the evolved velocity, and we use the filtered small scales to correct the large scales. Furthermore, in the new VMS-EF strategy, we use two different ways to decompose the evolved velocity: the VMS Evolve-Filter-Filter-Correct (VMS-EFFC) and the VMS Evolve-Postprocess-Filter-Correct (VMS-EPFC) algorithms. The new VMS-based algorithms yield significantly more accurate results than the standard EF in both the FOM and the ROM simulations of a flow past a cylinder at Reynolds number Re = 1000.