Defect-Deferred Correction Method Based on a Subgrid Artificial Viscosity Modeling

TL;DR

This paper introduces a subgrid artificial viscosity approach to enhance the defect-deferred correction method for incompressible Navier-Stokes equations at high Reynolds numbers, improving efficiency while maintaining stability and accuracy.

Contribution

The paper proposes a novel SAV-based first step approximation for DDC, demonstrating its advantages over traditional AV-based predictor steps in theory and computations.

Findings

Increased efficiency of DDC with SAV approach.

Maintains unconditional stability and high accuracy.

Outperforms traditional AV approximation in predictor step.

Abstract

An alternative first step approximation based on subgrid artificial viscosity modeling (SAV) is proposed for defect-deferred correction method (DDC) for incompresible Navier-Stokes equation at high Reynolds number. This new approach not only preserves all qualifications of the conventional artificial viscosity (AV) based DDC, such as unconditional stability, high order of accuracy and so on, it has also shown its superiority over choosing AV approximation in the predictor step. Both theory and computational results presented in this paper illustrate that this alternative approach indeed increases the efficiency of the DDC method.