On the sensitivity to model parameters in a filter stabilization technique for advection dominated advection-diffusion-reaction problems

TL;DR

This paper investigates the sensitivity of a filter stabilization technique with deconvolution-based indicators for advection-dominated ADR problems, focusing on parameter impact and robustness on a 2D benchmark.

Contribution

It introduces a three-step algorithm for applying filter stabilization to ADR problems and analyzes its sensitivity to key parameters compared to classical methods.

Findings

The technique is effective on under-refined meshes.

Parameter sensitivity significantly affects solution quality.

Deconvolution-based stabilization compares favorably with classical methods.

Abstract

We consider a filter stabilization technique with a deconvolution-based indicator function for the simulation of advection dominated advection-diffusion-reaction (ADR) problems with under-refined meshes. The proposed technique has been previously applied to the incompressible Navier-Stokes equations and has been successfully validated against experimental data. However, it was found that some key parameters in this approach have a strong impact on the solution. To better understand the role of these parameters, we consider ADR problems, which are simpler than incompressible flow problems. For the implementation of the filter stabilization technique to ADR problems we adopt a three-step algorithm that requires (i) the solution of the given problem on an under-refined mesh, (ii) the application of a filter to the computed solution, and (iii) a relaxation step. We compare our deconvolution-based approach to classical stabilization methods and test its sensitivity to model parameters on a 2D benchmark problem.